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Don't use an ICBM. Use an ASAT with a nuke as payload. These things have existed for decades.

Anti-satellite weapons (ASAT) are space weapons designed to incapacitate or destroy satellites for strategic military purposes. Several nations possess operational ASAT systems, with others in development or design. Although no ASAT system has yet been utilised in warfare, several nations have shot down their own (defunct) satellites to demonstrate their ASAT capabilities in a show of force.

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  ICBM is a bad pick. It can't track or be guided from the ground. You don't expect an enemy city to start running. I doubt, an alien ship will stand in place and wait for minutes for us to hit it. They would need to adjust the guidance system and give it ability to track targets.

How fast they can do that? Military will not tell me. It will be days, weeks even.

• ASAT & ABM can be used to deliver a nuke and have more guidance and precision for sure. Can they take it out? How durable is that ship? Can they chase that ship?




• Carrier rockets Use all we have, loaded with nukes. Will aliens allow you to set them up for a launch?




• EMP Will that work alone? I would think, an alien ship would have a lot of protection from that. At least we can try.

For better chances, I would make a "net" of missiles from all sides, with a good amount of decoys with no payload.

How fast? That would depend on our desperation and how hard that ship is to hit. Parts of defense can be used in minutes/hours. Same for some of ICBMs, if the ship will not evade them. Maybe, we have a Falcon 9 or a Soyuz ready on a pad. How fast you can load them with nukes and work out how to blow them up?

If you detonate a nuke in the emptiness of LEO you won't rely on the shock wave to deliver damage, but mostly on the EMP.

The test executed with Starfish Prime showed that the damage can happen at considerable distance, both in space and time.

The Starfish Prime electromagnetic pulse also made those effects known to the public by causing electrical damage in Hawaii, about 1,445 kilometres (898 mi) away from the detonation point. [...] The weaponeers became quite worried when three satellites in low Earth orbit were disabled.[...] In the months that followed these man-made radiation belts eventually caused six or more satellites to fail.

Therefore I would dare to say that you won't need cm accuracy. Take any rocket which can deliver the weight of a nuclear warhead to LEO (130 kg for a W80) and make sure it detonates. For comparison, a Falcon 9 has a payload of about 10000 kg, and I am pretty sure the most time would be needed to transport all the warheads to the launch facilities.

For good security I would also add some shrapnel like device to saturate LEO with physical debris, so that you can damage as much as possible of the released flying saucer.

It's all software.

At their apogee, missiles don't have any thrusters, they can't turn. Adding maneuvering thrusters to a MIRV would be infeasible to do quickly, since you are essentially designing a new spacecraft.

That means you won't be making any significant hardware changes to the missile and warheads. You can get-r-done in software, except for fuzing, but bombs having multiple interchangeable fuzes (detonators) is almost as old as bombs.

The whole rest of this answer is about fuzing,

Mostly nukes are fuzed for altitude, though impact fuses are an existing (though fairly evil) option. You won't get the chance to develop a RADAR style proximity detonator for a MIRV. They don't already have them, and up til now there'd never been a use for one, unless they happened to use a RADAR altimeter you could hack for the purpose. (I am not an expt on nuke fuzing methods, nor should I be.) Anyway you'l need a ton of them, so it needs to be something you can quickly implement.

Swarming

A starship will be just like any other point defense: its point defenses will have limits. If you heard the phrase "Interceptors are running hot" on Babylon 5, that is a warning that the enemy fire is coming faster than the interceptors can defeat it, and the ship will start taking hits.

Stalin said, "quantity has a quality all its own": a Soviet hallmark, not to mention an American one in WWII on both fronts. So it is right out of the playbook of both large nuclear powers: this swarm philosophy is why they are large.

Presumably an advanced translight enemy has heard of both A-bombs and orbital missiles. It can shoot down our missiles all day. You're betting the planet that they can't shoot down 500 in 5 seconds. All this to say, this "time on target" approach will require an awful lot of fuzes.

Another reason for a swarm is to shotgun, much like the Hedgehog in WWII, so maneuvering is not effective.

The bigger problem is the ones that miss

Ok, so you got him. Unfortunately, the ship's bits pelted the west Atlantic. That's not the unfortunate part. It's that his position when hit was over the ocean west of France. That's not it either, the unfortunate part is that 460 missed shots launched from the Dakotas pelted the Holy Lands ranging from the Dead Sea to Pakistan, including wild shots that landed in Macedonia (both), the Donbass, and an Ulster's farm field. No harm done, they were fuzed to not detonate if they missed the ship.

Oh wait. Have you read Tom Clancy's The Sum Of All Fears?

At this point, you might as well take a shovel to every major city. Because it's no longer a question of "if", but "when". Thanks, aliens.

So you see where fuzing is a big deal, and there really aren't any good answers.

• Detonating near the ground is out of the question, obviously.


• If you fuze to detonate them in space or high atmosphere, you get massive EMP that does damage to satellites and on the ground both. France would be knocked back to the stone age in a flash.


• I can't see a technical way to get the MIRVs to sabotage themselves as reentry vehicles, e.g. Deliberately enter facing backwards and burn up in atmo, not that a huge injection of plutonium into the sky would be particularly awesome either.


• Really your best bet out of a lot of unpleasant choices is to let them land with a thud, and take your chances with finding them all before another of Clancy's books turns real.

There have been a lot of good answers so far, but I will suggest two different possibilities.

Firstly, using nuclear weapons is actually inefficient in space. The explosion is a spherical emission of hard x rays, but with no atmosphere to convert the energy into a shockwave, the energy dissipates according to the square cube law.

Energy dissipating according to the inverse square law

What is needed is a way to focus the energy of a nuclear weapon to power a device or illuminate a target. During the 1950's the ORION nuclear pulse drive did just that, and a refinement known as the CASABA Howitzer theoretically took this even farther. You can read about this here, and taking this to the next level with HEAT type warheads powered by nuclear energy here.

So using a booster to bring a manoeuvrable bus into space to fire directed energy "bolts" or streams of liquid metal moving at about .03 c is likely to get their attention.

Orion Pulse drive units are a good way to visualize what a CASABA howitzer or nuclear HEAT round would look like

Of course this is dependent on being able to launch a booster into orbit and having the bus get close enough to release its payload. Most aliens have seen "Independence Day" on SBO (Space Box Office), so are unlikely to fall for that.

However, if we consider nuclear devices to be compact energy sources, then another approach comes to mind. During an underground nuclear test in the "Plumb Bob" series, one of the massive caps covering the shaft where the underground explosion took place was actually "popped off" by the explosion below. While only a single film frame shows the cap leaving its position, calculations suggested the cap was moving at about 5X Earth's escape velocity. In all likelyhood the cap was vapourized by the intense air friction (it was never found), but a suitably designed "cap" could be launched into space.

Imagine a "silo farm" with physics packages placed at the bottom of each one. The silos are filled with water and a specially designed cap placed on the top of each silo. The detonation of the device turns the water into plasma, coupling the energy of the device more efficiently to the cap, which is shot into space at @ 10X orbital escape velocity. Assuming the silos are placed under the projected orbital path of the spaceship, it will be pelted with objects moving at 78 km/sec. Some of the caps may weigh many tons, and even if they shatter in flight, the effect is a hail of shotgun pellets weighing between grams and multiple hundreds of kilograms. Good luck shielding against that.

And now the reason for all these silos becomes clear....

The knowledge exists, the real question is how much time would it take to convert existing nuclear warheads into the driving packages for either HEAT type warheads or to launch nuclear shotgun rounds at orbiting spacecraft? For that I really have no answer.

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  Retarget an ICBM. This might require a redesign of the Permissive Action Links, and ICBMs are not designed to reach orbit. They do reach orbital altitude, however.


• As suggested by Renan, use an existing ASAT. This could be tricky if the ASAT system was designed for kinetic kills, because adding the weight of a nuke would greatly affect performance.
  
  There is an off chance that some country still has a nuclear ASAT in storage.


• Put a nuclear demolition charge on top of a satellite launch system or resupply capsule. Craft like the ATV or Dragon are designed to dock with a station, surely they can ram an UFO.

For all of these options, you have to discriminate between "emergency operational capability" and a mature, reliable system. I will go out on a limb and say that IF the US, Russia, or China go into panic mode, they can launch something within a couple of weeks, possibly even within days. That would require a deliberate decision to ignore safety margins and simply go ahead. A 25% chance that the bird will explode on the pad and a 25% chance that it will explode in flight will still leave an over 50% chance to make it into orbit. France, Israel, or India would need a few weeks more. Not sure about the UK.

ICBMs have been used in the past to launch satellites, so they should be able to put a warhead in orbit as well. Of course safety mechanisms and detonation trigger would have to change a little, but that shouldn't take a long time.

If the enemy ship is orbiting its path is fairly predictable and a sophisticated SAM-style guidance would not be necessary. If the enemy ship can maneuver, the best bet would be un-mothball nuclear ABMs from 1980s (like A-350/ABM-1 Galosh for example), they were already designed to intercept moving targets and were equipped with fairly large nuclear warheads. If they don't have the range the engine can probably be extended or replaced.

As for how long it would take, with such systems normally the testing takes by far the longest time, if you forgo that and just hope for the best you can probably whip something up within weeks, or even days if it's just using stock ICBMs with modified trigger

Less than an hour.

ICBMs can be retargeted in a few minutes. Possibly even faster these days. The mission profile for a LEO burst most likely exists, because that's what it takes to use nukes as strategic EMP weapons.

The typical orbit insertion accuracy in a LEO mission seems to be a few kilometres these days. Based on that, a single missile would most likely miss, but there would be a good chance to hit the target with multiple launches.

The other options people have mentioned are not so good:

• Using orbital launch vehicles or missiles not designed to carry nuclear warheads would probably take weeks. New physical interfaces would have to be developed and new software would have to be written.


• ASAT missiles and other kinetic impactors would not do it. The maximum relative speed of a LEO impact is around 16 km/s. At that speed, the kinetic energy is 128 MJ/kg, or about 30 times the energy density of TNT. You would need a 30-ton impactor for the energy equivalent of a small 1-kiloton nuclear explosion.

No new technology is needed.

Just run a resupply mission for the international space station, with remote detonation nukes as cargo.

Instead of going to the ISS, go to the alien spacecraft.

You don't really want a nuke unless you want to use EMP effects on that spaceship.
Nuking the ship is difficult, as nukes cannot be properly set off while colliding with the ship, and every bit of distance redirects more of the blast energy to the empty space.

Yet, having as much mass as possible travelling as fast as possible relative to the target will deliver a lot of concentrated energy to the target without the need for a warhead.

20-ton rocket upper stage colliding with the spaceship at 15000 m/s on opposite direction orbit will deliver about half-kiloton of energy, all concentrated in the point of impact. This has a very high probability to demolish a thing as fragile as a spacecraft.

So what we should do is launch every vehicle able to reach target orbit and try to score a hit on it. This includes nukes, but we might want to replace their warheads with inert mass penetrators beforehand.