In 2008, Joe Robinson joined Ipswich Town at the age of 12. He progressed through the Ipswich Town youth sides and captained both the under-18 and under-21 sides. On 28 November 2015, following on from good form in the under-21 side, he was named on the bench in Ipswich Town’s 3-0 away victory over Charlton Athletic. On 19 January 2016, he made his senior debut in a 2-1 defeat to Portsmouth in the FA Cup.
On 22 February 2016, Joe joined National League side Woking on a one-month loan deal until 28 March 2016. His loan spell at Woking was extended until the end of the 2015/16 campaign but was cut short in mid April.
During August 2016, Joe Robinson joined National League North side Boston United on a one-month loan deal, to gain first-team experience. Joe made his Boston United debut in a 1–1 home draw against Kidderminster Harriers. His loan was extended as he went on to play 16 games for the Pilgrims, scoring once and being named man of the match in one game.
Joe signed for the Saints, on a one-month deal, at the beginning of March 2017. His loan was then extended to the end of the season.