Carson started his career with Ipswich Town's youth system in February 2009, before signing a professional contract in July 2010. He broke into the first team during the 2010–11 season, and was loaned to League Two club York City in March 2013. After being released by Ipswich, Carson joined York permanently in September 2013. He remained with York for three seasons before his release in 2016.
Carson signed for York City permanently on 12 September 2013 on a contract until the end of the 2013–14 season. His second debut for the club came two days later as a 63rd minute substitute for Sander Puri in a 2–1 home defeat to Mansfield Town. He scored his first goal for York in a 3–0 win away to Torquay United on 5 October 2013. On 13 February 2014, Carson signed a contract extension until the end of the 2014–15 season. He was released by York when his contract expired at the end of 2015–16.
On 3 August 2016, Carson joined NIFL Premiership club Linfield. He made 15 appearances, scoring 2 goals, as Linfield won the 2016–17 NIFL Premiership title.
On 11 May 2017, Carson signed for Linfield's NIFL Premiership rivals Coleraine on a two-year contract.
