A native of Swift Current, Saskatchewan, McCleary played junior hockey in the Western Hockey League (WHL) with his home-town Swift Current Broncos beginning in 1988. He played a total of four seasons with the Broncos, winning the WHL championship and Memorial Cup with the team in 1988–89 though he played only three games with the team. He was a defensive forward in the WHL, but scored 50 points in his final year in helping the Broncos win a second championship. He added a goal in four games at the 1993 Memorial Cup.