Born and raised in Lamesa, Texas, Corbin attended Texas Technical University, where he studied Drama. He moved to New York to pursue acting after spending two years with the Marine Corps. For nearly a decade, he starred in a string of stage productions before moving to Los Angeles. While writing plays for National Public Radio, he landed the role of Uncle Bob in the hit 1977 film Urban Cowboy, which launched his prolific career. Since that break, Corbin's well-known film roles have included War Games, Nothing in Common, The Best Little Whorehouse in Texas, Who's Harry Crumb? Career Opportunities, Ghost Dad, Curdled, Solo and Inconvenienced.

He has starred on Broadway, Off-Broadway and in regional theater in such roles as Henry in Henry V, Jud in Oklahoma, Henry II in Beckett, Falstaff in The Merry Wives of Windsor and Macbeth, among others. Corbin also performs a one-man traveling show he co-wrote called Charlie Goodnight's Last Night, about the celebrated Texas cowboy.

Corbin currently shares a ranch with his daughter and three grandchildren in Fort Worth, where they raise horses and cattle.