the missile would never hit the carrier.
a carrier is always on tour in a battlegroup which consist of missiles cruisers, warships, destroyers, frigates and submarines and their main goal is to defend the carrier.
such a battlegroup has water and air superiority in a range of around 500+ km.
You don't even know the basics of modern warfare.
Suppose the Russians launch an ICBM (either the SS-18 Satan or the SS-23 Spider) against an American aircraft carrier. How these missiles cruisers, warships, destroyers, frigates, submarines.etc are going to shoot it down? Right now there is no Ameircan anti-ICBM missile capable of shooting down a Russian ballistic missile.
Please stop googling your wisdom on wikipedia please.
Explain to me how a icbm works and how it should be able to hit a moving target at water in wartimes.
Why do you think they developed asbm's for this job?
Please explain it to someone like me that has no clue about modern (naval) warfare.
You see, before the us lets one of it carrier downed by a nuclear strike they already would have started a first strike for sure.