Cox, the third of five children, was born in Cloudcroft, New Mexico to Lounette Rucker and Bob P. Cox, a carpenter who also worked at a dairy. He grew up in Portales, New Mexico.

As an actor, he is probably best known for his debut performance as Drew Ballinger in the acclaimed 1972 film Deliverance in which he plays the instrumental "Dueling Banjos" on his guitar with a mentally retarded banjo-playing mountain boy named Lonny, played by child actor Billy Redden. Cox has also appeared as Lieutenant/Captain Andrew Bogomil in Beverly Hills Cop and Beverly Hills Cop II, Richard "Dick" Jones in RoboCop, Mars Administrator Vilos Cohaagen in Total Recall, and Senator/Vice-President/President Robert Kinsey in Stargate SG-1. Cox also portrayed John Ramsey in the 2000 TV movie Perfect Murder, Perfect Town.

Cox made a guest appearance on Star Trek: The Next Generation as Captain Edward Jellico in the two-part episode "Chain of Command". Recently he played Henry Mason, the father of Bree Hodge on Desperate Housewives. Between 1974-1975, Cox starred in the short-lived CBS family-oriented dramatic series entitled Apple's Way created by Earl Hamner. The program was based on a Los Angeles family who relocated to the father's hometown in Iowa with the hope of living a simpler, less hectic life-style.

Cox tours regularly with a band, performing at theatres and folk music festivals. On September 10, 1960, he married Mary Cox. She died in December 2006. They had two children.