The Canaries recalled the 20-year-old from his loan with MK Dons in order to send him to Rovers. Subject to EFL approval he is in line to make his debut against Cambridge United on Tuesday.
He made 12 appearances for Milton Keynes, with only four starts, as he struggled to break into the team following the departure of Russell Martin, whom he worked with previously at Norwich.
A former Arsenal youngster, Martin joined Norwich in March 2019. After impressing at youth level, he was involved in the senior squad in the final few months of the 2019/20 season and made five substitute appearances in the Premier League.
Last season he made 12 appearances as the Canaries won promotion from the Championship, including a run of six starts from seven league matches where he also grabbed his first senior league goal.
Martin was typically used in a wing back role with MK Dons but is more of an out and out winger that can operate on either flank.
He will wear the number 21 shirt during his time with Rovers.