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.
This IMDB search gives you all films which have
The following are the first elements of the list: