Aberdeen's reward for eliminating holders Celtic from the Scottish Cup is a home quarter-final against Dumbarton.
There is a potential all-Premiership tie with Dundee United visiting Stranraer or Inverness, with those sides replaying on 18 February.
Raith Rovers, who beat Hibernian at Easter Road, will host St Johnstone.
And Albion Rovers' first appearance in the tournament's quarter-finals since 1934 takes them to Ibrox to face Rangers.
The Wee Rovers overcame Stenhousemuir after causing a major shock by defeating Motherwell earlier in the competition.
Rangers were comfortable winners over Dunfermline in the first of the fifth-round ties on Friday.
And United claimed the final place in the draw with Sunday's win over St Mirren.
Scottish Cup quarter-final draw
Raith Rovers v St Johnstone
Aberdeen v Dumbarton
Stranraer/Inverness CT v Dundee United
Rangers v Albion Rovers