Baker, who stood 3 ft 8 in (112 cm) tall, was born and educated in Birmingham, Warwickshire, and at boarding school in Kent. His parents were of average height. He wanted to follow in his father's footsteps and be an engraver, but had not received sufficient education. He went to live with his father, stepmother and half sister in Hastings, Sussex, and in 1951 was approached on the street by a lady who invited him to join a theatrical troupe of dwarves and midgets. This was his first taste of show business. Later, he joined a circus for a brief time, learned to ice-skate and appeared in many ice shows. He had formed a successful comedy act called the Minitones with entertainer Jack Purvis when George Lucas hired him to be the man inside R2-D2 in Star Wars in 1976.
Baker appears as R2-D2 in six of the episodic theatrical Star Wars films, and played an additional role in 1983's Return of the Jedi as Paploo, the Ewok who steals an Imperial speeder bike. He was originally going to play Wicket, but he fell ill and that role was handed over to Warwick Davis. Baker is featured on Justin Lee Collins's "Bring Back Star Wars". He revealed a feud between him and his co-star Anthony Daniels. He claimed Daniels had been rude to him on numerous occasions, and states that Daniels is rude to everyone, including fans.
Baker's other films include The Elephant Man, Time Bandits (also with Jack Purvis), Willow (also with Purvis and Warwick Davis), Flash Gordon, Amadeus and Jim Henson's Labyrinth. On television, he appeared in the British medical drama Casualty.
He also had a part in the BBC production of The Chronicles of Narnia.