Rangers played a total of 28 competitive matches during the 1891–92 season.
The club began the season as champions but ended it in fifth position, winning exactly half of their 22 league matches.
The club were knocked out the Scottish Cup at the semi-final stage after losing to eventual champions Celtic by 3–5.
Rangers reached the final of the Glasgow Merchants' Charity Cup for the first time in eight years, but lost the final 2-0 to Celtic at Celtic Park.
All results are written with Rangers' score first.