Martin moved to Ibrox in 1958 and played 126 times - including 15 European ties - over 12 years while also spending spells as an understudy to George Niven and Billy Ritchie. He was in goal during the club's run to the 1966/67 European Cup Winners' Cup final, playing against Borussia Dortmund, Real Zaragoza, Slavia Sofia and Bayern Munich.
Martin was born in Ladybank and started his career with junior side Dalry Thistle and Hamilton Academical before coming to Rangers. He left the club in 1970 before winding down his career with East Fife, Queen of the South and Hamilton again.
Sandy Jardine, the former Rangers defender, told the club's website: "Norrie was at Rangers for a long time. He will be remembered for being part of the team that reached the European Cup Winners' Cup final in 1967 but he made over 100 appearances for the club. Had it not been for injuries and having to compete with likes of Billy Ritchie he would have undoubtedly made a lot more. It was very sad to hear that he had passed away after a short illness."