Rangers played a total of 41 competitive matches during the 1923–24 season.
The team finished top of the league, nine points ahead of second placed Airdrieonians, after winning twenty-five of the 38 league games.
The side was knocked out of the Scottish Cup in the third round that season.
After overcoming Lochgelly United and St Mirren, a 2–1 defeat to Hibernian ended the campaign.
All results are written with Rangers' score first.