The son of eminent surgeon A.O. Singleton, Sr., Dr. Singleton was born in Galveston, Texas in 1915. He graduated from the University of Texas at Austin in 1935 and the University of Texas Medical Branch four years later. After graduation Dr. Singleton spent a year each at the university hospitals in Philadelphia and Ann Arbor and four years in the military.

Before coming back to Galveston, Dr. Singleton was an instructor in surgery at the University of Michigan. He joined the faculty of University of Texas Medical Branch as an assistant professor of surgery shortly after his father's death in 1947. He became an associate professor in 1953 and held that position until his death in 1980.

Like his father, Dr. Singleton was a prolific writer who authored close to 80 journal articles alone. He also was a member of many scientific and surgical societies and served as the president of the society that bears his name.