McKay made his first-team debut for Rangers on 13 May 2012, in a 4–0 win against St Johnstone. On 11 August 2012, he scored Rangers first goal in the club's inaugural game in the Third Division, a 2–2 draw against Peterhead. On 11 September 2012, McKay pledged his future to Rangers for another five-years. After a great start to the season, his form dropped and as a result he was dropped to the bench with Fraser Aird taking his place. After a few matches on the sidelines, he reclaimed his place in the starting eleven with a stunning performance from the bench against Alloa Athletic, in which he scored two goals in a 7–0 win. From that point on, McKay established himself as a key player in the team, putting in several excellent performances, including in a 3–0 win against Elgin City and a 4–2 win against Montrose, racking up a number of assists in the process.