Born in Leicester, Leicestershire, Robinson began his career in the youth system at Leicester City. He made 43 appearances in the youth team over the course of two seasons, scoring 14 goals, but was not offered a contract and left the club in early 2012.
Luton Town
Robinson went on trial with Conference Premier club Luton Town later in 2012 and impressed manager Paul Buckle enough in pre-season to be offered a two-year professional contract. He made his debut as an 87th-minute substitute in a 2–0 win away to Kidderminster Harriers on 14 August 2012. Robinson made six substitute appearances and started two matches under Buckle, before starting six matches under new manager John Still following his appointment on 26 February 2013. He scored his first professional goal on the final day of 2012–13 in a 3–1 win away to Southport and finished the season with 14 appearances and one goal. In June 2013, Robinson signed a contract extension until June 2015. Robinson was primarily an unused substitute for much of the first half of 2013–14, though he did play in Luton's FA Cup and FA Trophy matches. On 26 December 2013, fellow Luton midfielder Jonathan Smith suffered a double leg break during a 2–1 win away to Barnet, promoting Robinson to a more regular place in the team. He played in all but one of Luton's matches in the second half of the season, scoring his first goal of 2013–14 in a 3–0 win at home to Chester on 22 March 2014, and this was followed up with a goal in the following match, a 2–1 win away to Grimsby Town. 19-year-old Robinson, who played alongside 18-year-old Cameron McGeehan and 20-year-old Pelly Ruddock Mpanzu in a youthful midfield trio, was praised by Still for his performances. He finished the season with 31 appearances and two goals, as Luton won the Conference Premier title and therefore promotion into League Two. He made his Football League debut in Luton's 1–0 victory away to Carlisle United on the opening day of 2014–15. On 1 October 2014, Robinson signed a three-year contract extension to keep him at Luton until June 2017. On 31 October 2014, Robinson joined Kidderminster Harriers on a one-month loan. He went on to make six appearances for the Harriers before returning to Luton, declining the chance to stay for a further month to fight for his place at Luton. He made a total of 12 appearances for Luton throughout the season, but was placed on the club's transfer list in May 2015 alongside five other players. On 21 August 2015, Robinson joined National League club Grimsby Town on a one-month loan. On 23 October 2015, Robinson joined Woking on a one-month loan after failing to impress at Grimsby Town. He debuted a day later, starting in a 3–0 defeat away to Maidenhead United in the FA Cup fourth qualifying round. On 19 December 2015, Robinson scored his first Woking goal in a 5–1 victory away to Gateshead, in which he poked home a cross from Dan Holman. On 14 January 2016, Robinson's loan at Woking was extended until the end of the season. He completed the loan spell with 31 appearances and two goals. On 10 May 2016, Luton announced that Robinson had once again been placed on the transfer list. However, just one week later, he was released from his contract by mutual consent one year early as part of the reorganisation of the squad by Luton manager Nathan Jones. He made 57 appearances and scored three goals since joining the club in 2012.
Dagenham & Redbridge
Robinson signed a two-year contract with newly relegated National League club Dagenham & Redbridge on 7 June 2016.