Currently, there is no publicly available technology which would permit one to time travel.
However, assuming one were to create such technology, is there any laws prohibiting time travel? I am interested in the various jurisdictions within the United States, but answers based on other jurisdictions would be interesting to read as well.
In theory, this should be protected by the UN Dec. of Human Rights:
Article 13 1. Everyone has the right to freedom of movement and residence within the borders of each State. 2. Everyone has the right to leave any country, including his own, and to return to his country.
Since it does not specify the type of movement, or restrict its dimensions, this could be construed to include freedom of movement through time as well as space.
Other than that things like this there is no real law regarding this.
The Telephone Consumer Protection Act was enacted on December 20, 1991: the act restricts phone spam. For almost a year after that, "text messages" were impossible, until the first text message was sent on December 3, 1992. The courts have held (Campbell-Ewald Company v. Jose Gomez, Keating v. Nelnet) that a text message is a "call" and thus prohibited in the relevant circumstance. Smith 2007 "Why originalism won't die" (2 DJCLPP 159), and millions of other authors, have noted that the law states what is legally permitted, in broad conceptual terms – it is not limited to just what happens to be possible right now, thus the First Amendment concept of "press" applies to things that were impossible at the time. (Whether or not patents can be issued that protect property rights to non-existent things is orthogonal). I am aware of no legal precedent for invalidating a law just because it describes something that cannot currently be done.
So it becomes a simple matter of searching all of the laws to see if there happens to be such a ban enacted. There is a microscopic level of support for the idea that China has banned time travel, though actually that seems to be a ban on TV shows with time travel. As far as I can tell, no legislative body has been so crazy as to ban time travel.
Your premise is flawed - it is possible to time travel - and more then 1 way to do so, and there are no laws prohibiting time travel.
The ways in which one can time travel include:
Under the constitution, United States Courts are prohibited from hearing and ruling on any legal case when there is no standing. Thus, for all US jurisdictions, determining the merits of a law restricting the use of time travel is moot without a demonstrable use of time travel as recognized by the courts. At this point, there is no current law on the books and any current violation of existing law cannot be ruled upon until time travel beyond the rate of one second per second is provable.
Similarly, the rights of Aliens, Vampires, and Sentient computer programs do not exist as of this moments as they have not been demanded by entities that hold standing to demand these rights and you cannot legally demand these rights for someone else. Chewbacca, Dracula, and Ultron must file these suits in a court of law in order to have them (Though Spock does have these rights, as he is half-human, and assuming his mother is a United States citizen).
In short, there are no laws which are legally tested to affect time travel in any positive or negative way as of time of writing and it is illegal to hear cases on such matters until time travel is demonstrably proven. Thus far, this leaves the only laws regulating time travel to the the ones found in physics text books. So remember, when dealing with space-time: 6.71 x 10^8 miles per hour: It's not just a good idea. It's THE Law!
If you travel back to before you reached the age of criminal responsibility, you cannot be convicted even if time travel is illegal. Authorities go by the time elapsed from your birth by normal Earth time when they decide if you are old enough to be punished for crime.
