Rodin studied saxophone, clarinet, flute, and trumpet as a youngster. He played in Chicago with Art Kahn in the middle of the 1920s. He moved to California and played with Harry Bastin before joining Ben Pollack in 1927, remaining in his band until 1934. Concomitantly Rodin did studio work and played with Red Nichols's radio band. He made his only recordings as a leader in 1930-31, amounting to four tracks which included Jack Teagarden on vocals, as well as Eddie Miller and Benny Goodman as sidemen.
After the dissolution of Pollack's band in 1934, Rodin played with some of the players in the group until Bob Crosby regrouped them into his own ensemble; Rodin remained with Crosby through 1942, when he was drafted. While serving in the Army Rodin played in the Artillery Band; after his discharge he played with Ray Bauduc (1944–45) and then Crosby again.
His major composition was "Big Noise from Winnetka", for which he wrote the lyrics with Bob Crosby. The music was written by Ray Bauduc and Bob Haggart. The song has appeared in the films Raging Bull (1980) directed by Martin Scorsese, the 1982 film Cannery Row, Woody Allen's Manhattan Murder Mystery (1993), Saving Mr. Banks (2013), and What If (2013).