If Ally McCoist's side can overcome James Ward's men on the weekend of March 8 and 9, they will also be at home for the semi-final as Ibrox will host both last-four clashes due to Hampden being unavailable because of the Commonwealth Games.
Rangers clinched their place in the last eight following Friday night's 4-0 win over Dunfermline Athletic where Dean Shiels grabbed a hat-trick.
With Old Firm rivals Celtic out of the competition after their 2-1 home defeat by Aberdeen, the Light Blues will fancy their chances of lifting the trophy this season.
The Dons will meet Dumbarton at home, with Raith Rovers at home to St Johnstone, and Stranraer or Inverness Caledonian Thistle hosting Dundee United, who beat St Mirren 2-1 at Tannadice on Sunday.
Raith Rovers v St Johnstone
Aberdeen v Dumbarton
Stranraer or Inverness Caley v Dundee United
Rangers v Albion Rovers
Ties to be played on weekend of March 8 and 9