rexe played junior hockey with the ontario major junior a, peterborough petes. in 1967, rexe was offered an contract by penguins general manager, jack riley, at $7,500 for one season with a $7,500 signing bonus. rather than sign with pittsburgh, rexe chose to join the canadian national hockey team as an amateur where he competed internationally for canada. at the 1968 winter olympics rexe backed up wayne stephenson on the way to a canadian bronze medal. canada withdrew from official iihf events in 1970 and the national team programme was suspended after they were refused permission to use semi-professional players at the world championship. rexe spent the rest of his hockey career playing in minor hockey leagues without ever appearing in an nhl game.