Rawson was born in Nottingham and began his footballing career at Derby County. On 3 June 2014 it was reported that Rawson had been offered a professional contract at Derby and would join the club's Under-21 team for the 2014–15 season.[5]
He was called up to the Derby first-team squad and was an unused substitute as Derby won 1–0 at Pride Park against Charlton Athletic in the second round of the League Cup on 26 August 2014.[6]
Rawson signed on a 28-day youth loan for fellow Championship club Rotherham United on 7 March 2015, making his debut the same day in a 2–0 away win against Huddersfield Town.[7][8][9] His loan spell at Rotherham expired on 4 April but he played against Brighton & Hove Albion two days later and subsequently Rotherham faced a charge for fielding an ineligible player. On 24 April, Rotherham were deducted three points and fined £30,000 for fielding him in that match.[10]
Rawson re-joined Rotherham on a six-month loan deal on 15 July 2015, along with teammate Kelle Roos.[11] Upon re-signing Rawson, then boss Steve Evans described Rawson as being a future Premier League player and was complimentary about the players performances on loan the previous season calling them "outstanding".[12] Rawson scored his first senior goal in a 1–1 draw against Charlton on 12 September 2015.[13] On 7 January 2016, Rawson's loan at Rotherham was extended until the end of the season,[14] however on 22 February 2016, a clause was activated allowing his immediate recall by Derby.[15]