The Scottish international with join the Ladbrokes Premiership side for the remainder of the season after falling out of favour with Norwich City.
The 32-year-old is still club captain at Carrow Road but has not played since a 4-0 defeat to Millwall in August.
Graeme Murty is keen to add more strength to his centre-back corps, while summer signing Bruno Alves has been linked with a move away from Ibrox in the January window.
Martin has been capped 29 times by Scotland. The English-born centre-back qualifies to play for the national side through his Scottish father.