Socolow began his career in the early 40s playing in swing bands led by Georgie Auld, Ted Fio Rito, Roy Stevens, Van Alexander and Shep Fields. In 1944 he landed the first of three stints (the others being in 1948 and 1956–57) with Boyd Raeburn‘s Orchestra, recording a number of records. In 1945 he recorded a session as leader (the first of only two) with Freddie Webster and a young Bud Powell for Duke Records.
He was a member of Buddy Rich‘s short-lived big band, toured Scandinavia 1947-48 with Chubby Jackson, joined Artie Shaw‘s big band 1949-50, and throughout the late 40s and the 50s recorded with a wide variety of artists including the aforementioned, Johnny Bothwell, Charlie Ventura, Gene Krupa, Sal Salvador, Maynard Ferguson, Terry Gibbs, Phil Woods, Cecil Payne, Manny Albam, Hal McKusick, Johnny Richards, Bill Russo, Joe Morello, and Bobby Scott. His second record session as leader, and only full album release, Sounds by Socolow, came in 1956 for Bethlehem Records, with arrangements by Bill Holman, Manny Albam, and Sal Salvador, the latter also contributing guitar. Socolow died in New York in 1981.