Playing rugby at both Knox Grammar School and Sydney University, Stirzaker was signed to be a part of the Rebels extended playing squad during the 2012 season only playing a total of three games all coming off the bench. After his debut season as an extended player, Stirzaker played eleven games for the Rebels throughout 2013, starting twice and coming off the bench on nine occasions. On 25 June 2013, Stirzaker come off the bench in the 55th minute to play for the Rebels against the British & Irish Lions during their 2013 tour in a 0–35 defeat at AAMI Park, Melbourne. In March 2014, Stirzaker re-signed with the Rebels until the succession of the 2015 season. Stirzaker was subsequently released to Palmerston North-based ITM Cup team Manawatu Rugby Club for the 2013 season. Finishing the season fifth in the Championship division, Stirzaker scored a total of three tries before returning to the Rebels in 2014. Sustaining an injury before the 2014 season, Stirzaker only played eight of the sixteen games, starting in just four. After a fairly successful 2015 season for Stirzaker – playing fifteen games, scoring three tries, and helped lead the Rebels to a tenth position – he was among rumours of a possible call up to the Wallabies squad. Stirzaker is eligible to represent three countries internationally. Australia, England, and South Africa. In early 2016, Stirzaker was announced as captain of the Rebels ahead of the season. He had undergone off-season shoulder surgery causing him to miss the season-opening match of the 2016 season against the Force in Perth. Stirzaker returned to full fitness to play the in 17–21 victory in round 6 at Allianz Stadium, Sydney. He played a total of eleven games scoring two tries.
In late January 2018 Bristol Rugby announced that Stirzaker would join them for the upcoming 2018-19 Premiership Rugby season.
Montauban
Ahead of the 2020–21 season Stirzaker joined French side Montauban.
International
Stirzaker was selected and played for Australia XV that played the French Barbarians in late 2016 losing 19–11 in Bordeaux. After previous successful seasons Stirzaker captained a Rebels team that finished wooden spooners for the 2017 season, and faced possible axing out of the competition.
