Rangers played a total of 22 competitive matches during the 1896–97 season.
They finished third in the Scottish League Division One with a record of 11 wins from 18 matches.
The club won the Scottish Cup that season.
A 5–1 victory of Dumbarton on 20 March 1897 saw them win the trophy for only the second time in the club's history.
All results are written with Rangers' score first.