Hinnant's first major role was as Cathy's boyfriend Ted on The Patty Duke Show from 1963 to 1965, and Schroeder in the original cast of You're a Good Man, Charlie Brown during its original off-Broadway run in 1967 (where his brother, Bill, played Snoopy).

He is best known as a featured performer on the children's show The Electric Company, which aired on the American educational television network PBS from 1971 to 1977. He was best known at that time as word decoder, Fargo North. He was also the voice of R. Crumb's underground comic character Fritz the Cat in both the X-rated animated movie of the same name and its sequel, The Nine Lives of Fritz the Cat.

His most recent acting role was a part in an episode of Kate & Allie.

Hinnant is the longest-serving President of the New York branch of the Screen Actors Guild.