The 32-year-old Scotland international has not featured for the Sky Bet Championship side since August and has become Graeme Murty’s fourth signing as Rangers manager following the loan arrivals of Sean Goss, Jamie Murphy and Jason Cummings.
Murty knows the defender well from his time as a youth coach at Carrow Road and the Canaries are happy for Martin to leave the club on loan during this window.
Martin started his career with hometown club Brighton and Hove Albion, but left the Seagulls by mutual consent towards the end of 2004, joining Lewes on a short-term basis.
After a trial spell with Charlton Athletic, Martin joined Wycombe Wanderers in 2004, spending four years at Adams Park and scoring five goals in 142 appearances, before joining Peterborough United in 2008.
Despite making 46 apeparances in his first season with The Posh, Martin spent time on loan at Norwich City the following season, before joining the Canaries on a permanent deal in January 2010.
He made more than 300 appearances for Norwich in all competitions, scoring 17 goals.