I was hoping to get some technical answers to this question, and was really asking because I thought it'd be a fun question. Have at it folks.
Yes, time travel is compatible with the general theory of relativity. This could be achieved, for example, with wormholes or Alcubierre drive. Krauss's The Physics of Star Trek book provides a popular exposition of some of these ideas.
However, GR is not the only physics at play, and there's reason to believe that when quantum effects are taken into account, these time travel mechanisms will cease to be possible. But until we have a quantum theory of gravity we won't know for sure.