The last time the sides met in the competition was in April 2011, when the Hoops triumphed with a 4-0 semi-final victory.
Neil Lennon's men have come out on top in both league meetings this season, while the Dons have booked their place in the last four of the League Cup.
With no Old Firm clash this time, Rangers were also handed a home tie and will take on the winners of the replay between Ayr United and Dunfermline.
The Ibrox side have defeated both clubs in Scottish League One action already this term.
League Two outfit Albion Rovers were rewarded with a home meeting against Stenhousemuir after pulling off the shock of the last round with a 1-0 victory over Motherwell.
Hibernian will play host to Raith Rovers and Dumbarton will travel to Alloa.
The remainder of the ties have yet to be decided, with Inverness visiting Clyde or Stranraer, Brechin or Forfar hosting St Johnstone and Dundee United at home to Queen of the South or St Mirren.
The ties will be played on the weekend of February 8/9.
- Sports & Recreation
- Ayr United
- Albion Rovers