While attending university, Irwin played two seasons with USL PDL club Carolina Dynamo. After his time at Elon, Irwin joined Capital City of the Canadian Soccer League for the 2011 season. Irwin made 22 appearances for Capital City and scored a goal for the club in a 2–2 draw with Windsor Stars. Following his stint with Capital City, Irwin joined his hometown club, the Charlotte Eagles of the USL Professional Division. On July 6, 2012, Irwin made his debut in a 2–0 win over the Charleston Battery In February 2013, Irwin signed with MLS club Colorado Rapids after a successful preseason trial. In January 2016, Irwin was traded to Toronto FC in exchange for targeted allocation money, a third-round pick in the 2016 MLS SuperDraft and a conditional first-round pick in the 2017 MLS SuperDraft. After featuring as the club's starting goalkeeper for the first part of the season, Irwin sustained in injury in July, and as a result, he was replaced by his deputy Alex Bono in the starting line-up by manager Greg Vanney; Upon his return to action, Irwin later regained the starting spot for the remainder of the regular season and the Playoffs, as Toronto went on to reach the 2016 MLS Cup Final. In the final, held at BMO Field on December 10, Toronto were defeated by the Seattle Sounders 5–4 on penalties, following a 0–0 draw after extra time; Irwin was able to stop Álvaro Fernández's spot kick during the shootout, but misses from teammates Michael Bradley and Justin Morrow ultimately proved to be decisive. On December 13, 2016, Irwin was selected by Atlanta United FC in the third round of the 2016 MLS Expansion Draft, but was immediately traded back to Toronto for Mark Bloom and allocation money. The following season, Irwin suffered a hamstring injury in the Toronto FC's home opener on March 31, a 0–0 home draw against Sporting Kansas City; as a result, Bono was once again promoted to the starting line-up in Irwin's absence, and eventually established himself as the team's outright first-choice shot-stopper by September 2017, due to his performances, even after Irwin's return from injury. In a rematch of the previous season's MLS Cup Final, on December 9, Toronto defeated Seattle 2–0 at home to capture the 2017 MLS Cup, and complete an unprecedented treble of the MLS Cup, the Supporters' Shield, and the Canadian Championship. Following the 2018 season, Irwin was traded back to the Rapids in exchange for a second-round pick in the 2019 MLS SuperDraft.
