He was born in De Valls Bluff, Arkansas, to a musical family: his father, Luddie Stidham, played with Jimmie Lunceford, and his uncle with the Memphis Jug Band. Arbie learned to play the harmonica, clarinet and saxophone as a child. Before his teens he had formed a band, the Southern Syncopators, which backed Bessie Smith on tour in 1930 and 1931 and played on the radio and in clubs in Arkansas and Memphis, Tennessee.
In the mid-1940s Stidham moved to Chicago, where he met Lester Melrose, who signed him to a recording contract with RCA Victor in 1947. His biggest hit, "My Heart Belongs to You", was recorded at his first session; it reached number one on the Billboard R&B chart in June 1948. He spent the rest of his career trying to achieve the same success, recording for Checker, States, and other independent record labels as a jazz-influenced blues vocalist.
He was in a car crash in the 1950s, and his Injuries made it impossible for him to play the saxophone, so he took up the guitar, under the tutelage of Big Bill Broonzy, and played it on recordings for Folkways Records in the early 1960s.
He recorded occasionally until the early 1970s and appeared at music festivals and clubs in the United States and abroad. He lectured on the blues at Cleveland State University in the 1970s. He appeared in the film The Bluesman in 1973.