Born Joyce Audrey Botterill in Northampton, Northamptonshire, England, the daughter of a London fruit merchant, Carne made British television appearances in series including Danger Man (1961). She moved to the United States in the early 1960s. Her first regular role was in the sitcom Fair Exchange, in which she played an English teenager who goes to the U.S. to live with an American family whose daughter (played by Lynn Loring) has gone to live in England. That was followed by The Baileys of Balboa (1964) and then she had an assisting role to Pete Duel in Love on a Rooftop (1966). She made appearances in the TV show The Man from U.N.C.L.E.. She had a small part in the ninth episode of the 1965 TV series Gidget, guest-starred as Floy in second season episode 3, "Then Came The Mighty Hunter" of 12 O'Clock High (1965), and appeared in an episode of I Dream of Jeannie. She also appeared in the Bonanzaepisode "A Question of Strength" (1963) as Sister Mary Kathleen and The Americanization of Emily (1964) plus two episodes of "The Big Valley" (1967.)
On Rowan & Martin's Laugh-In (1968–73) Carne gained stardom. Her most popular routine ended with her saying "Sock it to me!", at which point she was doused with water or in some other way assaulted. Carne was on the series for the first two seasons (1968–69) but made occasional appearances during the 1969-70 season.
Carne was married to actor Burt Reynolds from 1963 to 1965, and producer Robert Bergmann from 1970 to 1971.
Her autobiography, Laughing on the Outside, Crying on the Inside: The Bittersweet Saga of the Sock-It-To-Me Girl (1985), chronicled her difficulties with drugs, her failed marriage to Reynolds, and her bisexuality.