Rangers played a total of 37 competitive matches during the 1907–08 season.
The side finished third in the league, five points behind champions Celtic, after winning 21 of the 34 matches.
The Scottish Cup campaign was ended at the hands of the league champions after a 2–1 home defeat.
Rangers had drawn with Falkirk away and won the replay en route to the second round.
All results are written with Rangers' score first.