Carver was one of the earliest flute soloists to perform jazz; while Alberto Socarras preceded him by about five years, Carver was one of very few jazz flautists active in the swing era. His first professional experience was with J. Neal Montgomery. After he moved to New York City in 1931, he recorded with Dave Nelson, and played with Elmer Snowden (1931–32), Benny Carter, and Spike Hughes (1933).
From 1934 to 1939 he played with Chick Webb on both saxophone and flute. After Webb died he continued in the orchestra during its period of leadership under Ella Fitzgerald until 1941. After leaving the jazz scene he became a professor of music at Clark College, where he taught saxophonists George Adams and Marion Brown, among others.