Rawson played for Chesterfield's youth team, hitting headlines when he scored for the team's reserves as a 16-year-old in 2017.[2] He made his senior debut for the 'Spireites' in their final EFL League Two game of the 2017–18 season while still a first-year scholar, coming off the bench as an 82nd minute substitute for captain Drew Talbot.[3]
In September 2018, Rawson joined Matlock Town on a one-month loan deal.[4] He joined Sheffield on loan in December,[5] before returning to Chesterfield to make two appearances.[6] He rejoined Sheffield on loan in January 2019.[7]
In August 2019, Rawson once again joined Matlock town on a one-month loan deal.[8]
On 14 October 2019, Rawson joined Brighouse Town on loan until January 2020.[9] On 31 January 2020, he was then loaned out to Handsworth until 28 April 2020.[10]
On 2 August 2021, Rawson returned to National League North side Bradford (Park Avenue), this time on a permanent deal following his release from Chesterfield.[13] On 28 January 2022, he was sent out again to Sheffield, dropping down two divisions to play in the Northern Premier League Division One East for a month-long loan.[14] In February, this loan was extended until the end of the season.[15]
^One appearance one goal in FA Trophy, two appearances in Sheffield & Hallamshire Senior Cup, one appearance in Northern Premier League Division One East play-offs