A strong, assured left back,[3] Orr's influence as a leader shone after he became Celtic captain in 1902 and he led the club to three further league championships and two more Scottish Cups, including a double in 1906–07.
[4][5] He scored one of his team's three goals in the 1907 Scottish Cup Final;[6] however, a new younger signing, Jimmy Weir, then took over as first-choice at left back.
[7][8] Although his usual playing position at Celtic was in defence, he had been a half-back early in his career, and it was in this role that he received all his international caps.
[10][11] His success at Airdrie prompted the interest of English side Leicester City to replace the outgoing Peter Hodge.
Leicester began to decline after the loss of inspirational captain Johnny Duncan, who was deemed to have terminated his own contract after breaking the club rules in taking over the licence of a local public house.