Curtis, who was born in Brentwood, Essex and attended Shenfield High School, began his career with Tottenham Hotpsur where he was a member of the Academy. He briefly joined Maldon Town, before he joined Colchester United's Academy to continue his development ahead of the 2011–12 season. He signed his first professional contract with Colchester in November 2013. In the same season, Curtis helped the under-18 side to the Football League Youth Alliance South East title, while he also featured in the Youth Alliance Cup final held on 29 April 2014 at Bradford City's Valley Parade stadium. He played for 85 minutes in the final against Bradford as his side won 4–2 to complete a league and cup double. In the 2014–15 season, Curtis saw his first involvement with the first-team squad when he was named on the bench by manager Joe Dunne for Colchester's League Cup first round fixture with Charlton Athletic on 12 August 2014. However, he was an unused substitute in the 4–0 defeat. With his contract set to expire at the end of the season, Curtis signed a one-year contract extension on 8 May 2015. Following good form at under-21 level, Colchester manager Tony Humes named Curtis amongst his substitutes for their FA Cup first round tie with Wealdstone on 7 November 2015. With his side 6–2 up, Curtis replaced Macauley Bonne for his professional debut in the fourth minute of second-half stoppage time. He was offered a new deal at the end of the season, and agreed a one-year contract extension on 26 May 2016. Curtis joined Isthmian League Premier Division side Needham Market on loan for one month on 13 August 2016. He scored after just ten minutes of his debut as Needham were held to a 1–1 draw with Burgess Hill Town. He had his loan extended for a further month on 10 September, and his loan was further extended on 13 October. He scored six goals in 24 appearances. On 18 January 2017, Curtis was allowed to leave Colchester after six years with the club. In March 2017, Curtis signed for Isthmian League Premier Division side Harlow Town. He made five substitute appearances for the Hawks, but was released in June 2017 after failing to hold down a place in the starting eleven. After a spell with Coggeshall Town, Curtis joined Braintree Town in February 2018 on a dual registration basis.
