Robinson graduated from the National Institute of Dramatic Art (NIDA) in 1981, and appeared in theatrical productions in Australia and overseas, television shows such as Sons and Daughters (1986-1987) and films, including Moulin Rouge (2001).
He was part of the original Company B ensemble at Belvoir Street Theatre, which also included Hugo Weaving, Geoffrey Rush, Richard Roxburgh, Gillian Jones, Arky Michael and Paul Blackwell.
In 2006, after a diagnosis of a variant of Guillain-Barre Syndrome, a rare autoimmune condition, he took a ten-year hiatus from acting. He returned in the 2016 Eamon Flack production of Twelfth Night, in which he acted Feste (still using a wheelchair).