Sloane's Broadway theatre career began with the comedy Boy Meets Girl in 1945 and ended with From A to Z, a revue for which he wrote several songs, in 1960. In-between he acted in plays such as Native Son (1941), A Bell for Adano (1944), and Room Service (1953) and directed the melodrama The Dancer (1946).
In the 1940s, Sloane was a frequent guest star on the radio theatre series Inner Sanctum Mysteries and was in The Mysterious Traveler episode "Survival of the Fittest" with Kermit Murdock. In 1958 he played Walter Brennan's role in a remake of To Have and Have Not called The Gun Runners.
Sloane also worked extensively in television; in November 1955 he starred in the Alfred Hitchcock Presents episode "Our Cook's Treasure"; he was the voice of Dick Tracy in 130 cartoons produced in 1960 and 1961. Beginning in 1964, he provided character voices for the animated TV series The Adventures of Jonny Quest. He wrote the unused lyrics to "The Fishin' Hole", the theme song for The Andy Griffith Show. He starred as the ruthless businessman in both the film and television versions of Rod Serling's Patterns, and later guest starred in the first season of The Twilight Zone as the victim of a Las Vegas Slot Machine.