Baker, at 3 feet, 8 inches (112 cm) tall, was a circus and cabaret performer with entertainer Jack Purvis when George Lucas hired him to be the man inside R2-D2 in Star Wars in 1977. Baker appears in five of the six Star Wars films;though credited on Episode III, he never filmed any scenes. George Lucas decided to credit him in the film out of loyalty. Baker even played an additional role in 1983's Return of the Jedi, when he played Paploo, the Ewok who stole an Imperial speeder bike. He was originally going to play Wicket W. Warrick, but he fell ill, and that role was handed over to Warwick Davis.

Baker's other films include 1980's The Elephant Man, 1981's Time Bandits, 1984's Amadeus and the 1986 Jim Henson film Labyrinth.