There have been many characters who have travelled through time but who was the first? Off the top of my head, I can only think of Ebenezer Scrooge and his 3 ghostly visitors. I'm not even sure that they qualify.
According to this Wikipedia list of time travel in science fiction writing, film & tv, the 1949 adaption of A Connecticut Yankee in King Arthur's Court is the first example of time travel in a film or tv sci-fi work. I can't speak to the completeness of the list.
Interestingly, that list categorizes Charles Dicken's 1843 A Christmas Carol as sci-fi and includes the 2009 film adaptation in the film list. Based on the Wikipedia entry for the first film adaption, Scrooge, or, Marley's Ghost (1901), I don't believe the characters traveled through time in that particular adaptation:
It's unclear if the spirits showed Scrooge visions in the present or if Scrooge actually travelled through time with the ghosts.