Orr was born in Dublin. Educated at The High School, Dublin, and Trinity College Dublin, Orr played for Old Wesley for over 20 years and was, for many years, his country's most-capped prop with a then world record 58 appearances. Orr made his debut against France in 1976 and was part of the Irish teams that won a Triple Crown in 1982 and 1985. He toured with the Lions to New Zealand in 1977, winning one cap, but was not available for the 1983 tour to the same country due to business reasons. He retired from international rugby in 1987 having played for Ireland in the inaugural rugby world cup.
He was president of Old Wesley in its centenary, 1991. He is currently (2007) manager of the Irish U21 rugby squad.