The Third Division Ibrox side were drawn at home to Inverness Caledonian Thistle while Celtic will face St Johnstone at home.
Rangers are the only non-SPL side still in the competition and some of their fans had warned of boycotting the quarter-final if they had been drawn away.
The full draw is: Aberdeen v St Mirren, Rangers v Inverness, Dundee United v Hearts and Celtic v St Johnstone.




