Robinson joined Fulham on August 20, 2020. On September 16, he made his Fulham debut in a League Cup match against Ipswich Town, which Fulham won.

On September 23, he won 2-0 against Sheffield Wednesday in the next round. On October 1, he appeared in a 3-0 league cup loss to Brentford. On October 4, he made his Premier League debut against Wolverhampton.

On August 24, 2021, he scored his first goal for the club in an EFL Cup match against Birmingham City. He signed a new deal with Fulham until 2028 in July 2023.