THE ANSWER
No, Darth Vader does not say “Luke, I am your father.” The actual line is “No, I am your father.”
WHAT WE FOUND
In the first three released films Star Wars films, episodes IV through VI, Darth Vader is the primary antagonist while Luke Skywalker is the main protagonist.
The line in question is said in Star Wars: Episode V – The Empire Strikes Back. The movie came out in 1980 and was the second film released in the franchise. It is the highest critically-rated film of the Star Wars saga on Rotten Tomatoes, with a 94% “certified fresh” tomatometer score.