Born in Brooklyn, New York, Wexler served in the United States Army during World War II from 1943 to 1945, landing in France in August 1944. He served with an anti tank unit and was wounded by shrapnel a few days prior to the Battle of the Bulge. For his service he was awarded two Bronze Stars and a Purple Heart. He received a Bachelor of Science degree from Indiana University Bloomington in 1947. He received a Juris Doctor from New York University School of Law in 1950. He was in private practice of law in Bay Shore, New York, from 1950 to 1956. He was in private practice of law in Smithtown, New York, from 1956 to 1983. He was the administrator of the New York State Assigned Counsel Plan from 1966 to 1983.