Rangers played a total of 21 competitive matches during the 1892–93 season.
They finished second in the Scottish League behind first-time winners Celtic, with a record of 12 wins from 18 matches.
The club ended the season without the Scottish Cup after being beaten at the quarter-final stage by St Bernard's, 3–2.
They had previously defeated Annbank United and Dumbarton during the cup run.
All results are written with Rangers' score first.