Crosbie has represented Ireland internationally at under-age level. He was part of the Ireland under-20 team for the 2013 season, making his debut against Wales in the 2013 Six Nations Under 20s Championship. In May 2013, Crosbie was named in the Irish squad for the Junior World Championship. He featured in all five of the team's games in the tournament, taking his total number of appearances for the under-20 side to 13.