He worked as a stunt man and had a few acting roles in his twenties. One of his first roles was as an outlaw named Tom Sanger in an episode of the Western series Colt .45 in 1960.
Michael Gregory originated the role of Rick Webber on General Hospital, playing the character from 1976 to 1978. Robinson took over after Gregory left the show and continued playing Webber until 1986. Robinson then reprised the role in 2002 and again in 2013.
He married actress Jacquie Robinson and he has a total of five sons. His son Taylor Joseph Robinson was also cast on The Bold and the Beautiful.
He had a starring role alongside Paul Burke on the World War II drama series 12 O'Clock High from 1965 to 1967.