Yes, but homing on a moving target hundreds of miles away is no easy feat. The missile obviously can't do this by itself (like an air-to-air missile). It needs external guidance. There is no radar that has this type of range so you either need a satellite, or an AWACS airplane. In other words, the kill-chain will be quite complex. You can bet there are multiple countermeasures that can disrupt such a kill-chain (shot down the AWACS airplane, blind the satellite with laser, jam the spectrum for the incoming missile, deploy a smoke screen, etc). The simple indication that the "carrier killer" missiles are not such a sure thing is that the Chinese are busy building aircraft carriers themselves. Are they really stupid?