William C. Rank (June 8, 1904 – May 20, 1979) was an American jazz trombonist.
Rank was born in Lafayette, Indiana, on June 8, 1904, and initially worked in Indiana and Florida. Between 1923 and 1927 he played with Jean Goldkette's band in Detroit and often recorded with Bix Beiderbecke. After playing with Adrian Rollini in 1927 and a period as a freelance, Rank joined Paul Whiteman's band, and stayed until 1938. He was then a studio musician in Hollywood into the early 1940s, when he moved to Cincinnati. There, he led a tenet for the rest of the 1940s.
Rank then changed to playing part-time while also working in insurance. His one album as a leader, a tribute to Beiderbecke, was recorded in 1973. Rank continued playing until a short time before his death, on May 20, 1979, in Cincinnati.