EDIT: What was I thinking? A nuclear-tipped cruise missile is even better.
There are a variety of missiles which could potentially sink an aircraft carrier. ICBM has the longest range with the largest expense. Torpedoes (not really a missile) have a much shorter range so presumably the old principle applies -- if you can keep subs at a distance your carrier will be safe.
In other words, what you want to hit a carrier is the cheapest missiles where the launching platform (which could be a sub) are outside the range of the enemy, to present the largest quantity of missiles in order to overwhelm the defenses of the carrier.
ICBMs are most likely not the best way to do this, given their expense, but are worth bringing up since the basic principle is the same as in the cold war (shoot lots of ICBMS at a city/country to assure that some will get through).
Also, I believe whether or not any of the armaments are nuclear is fairly irrelevant since a non-nuclear missile (or two or three) can sink a carrier easily enough. That said, sooner or later someone (e.g. N. Korea) will use a nuke, and then all bets are off.
Nuclear torpedoes usually sink two ships - one of them is the target.