I am sure you could, however, you might not get too far. I am sure the Capt of the aircraft carrier would deny you access to his/her ship. If you just tried to land, you would probably be shot down before getting there.
Even if you were authorized, you might be able to stop before falling off the ship. Since the Cessna probably wouldn't have the tail-hook, then the Cessna would have to stop pretty quickly.
Also, it would depend on how far away the ship was at sea. And you would have to know where the ship was located to know where to go. If all that did work out, then I guess it could.
Also, keep in mind, its a film. If you want to land a Cessna on an Aircraft Carrier, write it in the story. If your story gets made into a movie, the scene will happen, whether real or not. Look at all the movies out there, the stunts that are performed is all done in the editing room. Yes, they do the stunts, but usually it takes a few takes ,and then they piece together the end result.