The season saw the club play in a league set-up for the first time in its history.
Rangers played a total of 20 competitive matches during the 1890–91 season.
They were the joint winners of the first ever Scottish League, sharing the title with Dumbarton.
The club's drew the championship play-off 2–2, so both were awarded the title and declared champions.
The club ended the season without the Scottish Cup after being knocked out by Celtic in the first round by 1–0.