After progressing through Leeds United youth ranks Dawson signed a professional deal at Leeds United keeping him at the club until the summer of 2015. Dawson was named as an unused substitute in three first team matches, during this period manager Neil Warnock compared Dawson's style of play and ability to that of former Leeds United legend John Giles. Dawson was given his debut for the Leeds first team by Neil Warnock on 1 April 2013, starting the 2–1 loss against Derby County, he was substituted in the 55th minute for Ross McCormack. Shoulder surgery ended Dawson's season prematurely, however, Dawson signed a new three-year contract with the club on 8 May 2013. Dawson returned to the Leeds United first team squad for the second time, ironically also against Derby County on 2 May 2014 for the final game of the 2013–14 season. After playing with Leeds' first team during the 2014–15 pre-season, on 30 July 2014 Dawson scored a hat trick for Leeds in the 5–0 pre-season victory in the friendly against Glenavon. On 1 August, Dawson was assigned the Leeds number 24 shirt for the 2014–15 season. On 1 November 2014, Dawson made his first appearance for the first team since his debut, when he came on as a substitute in Neil Redfearn's first game as permanent head coach in a 3–1 loss to On Cardiff City. Dawson was not included in United's 25-man travelling squad for the 2015-16 pre-season. On 31 July 2015, Dawson was not assigned a Squad Number for the upcoming 2015/16 season. Dawson was released from his Leeds United contract on 26 January 2016.
Rotherham United
On 28 January 2016, Dawson signed a contract with Rotherham United until the end of the 2016–17 season. Dawson was released by the club at the end of his contract, having not played a game for the club.
Viking loan
On 17 August 2016 Dawson went on loan from Rotherham to Norwegian club Viking FK until the end of 2016. Dawson made his debut on 21 August in Viking's 2–1 away defeat to Tromsø IL in Tippeligaen, coming on as a 65th-minute substitute for Samuel Adegbenro.
On 25 July 2018, Dawson joined National League North side Bradford on a permanent deal, after impressing initially on trial. On 10 February 2019, Dawson was loaned out to Grantham Town for one month. On 14 March, the deal was extended for the rest of the season.
Return to Scarborough
On 10 July 2019 Scarborough Athletic announced, that Dawson had returned to the club.