acquiring the target is the hard part, but that said,its not impossible, various ways can be deployed, from satellites to UAVs. and of course it will be maneuverable, there is research on maneuvering warheads by shifting the internal center of mass(that is to say, no need for fins and such).
Actually, if you have tried to tack somrthing in battlefield, you would know how difficult to even track a naval vessel as big as an aircraft carrier.
First of all, when you started using Ballistic missile, you are lready in war. meaning they are legally capable to shoot down all hostile or non-hostile target within a certain radius called exclusion zone winthin the ship. Your best bet is using the Satellite as everything range from fighter recon, awacs, uav can be shoot down very easily. But the downside of using satellite is, you can only track the target with a maximal of 10 minutes, as you know satellite will not and cannot stop and hovering on the same place, they are following the earth orbit, once the satellite are out of LOS, you cannot track the target anymore. Not to mention you can jam the satellite signal as well.
on the other hand, every minutes the missile airborne, you need to rack and correct the target coordination to alter the course bit by bit and as the last stage is an unassisted flight, meaning is if there are any update skipped, your missile is not going to lock on to the target.
Really difficult to operationalize........will be prone to failures(targets being missed ).......one thing u have to consider.........when the conflict goes ballistic, all satelite help will be finished( either to jamming or destroyed). Keeping track of the ACC all the time during flight will be quite difficult....
That's why in my assessment, ASBM is for show only, there are not much use if one can afford a big navy. Yes, this is very cost effective way to save up money, but it is not an effective way because there are complexity on their targetting system and all of it can be exploited.
