The Light Blues made an emphatic start to life under Mark Warburton at the weekend, winning 6-2 in his first game in charge at fellow-Scottish Championship title contenders Hibernian.
Now they will face former Rangers defender Ian McCall’s side at the next stage, with the game initially scheduled for August 18 or 19 but subject to change for live television coverage.
The competition remains regionalised at this stage and the tie of the round sees last season’s winners Livingston go to Queen of the South in the only all-Championship tie.
Speaking after the draw at Hampden Park, former Brentford boss Warburton said: “You want to win any competition you enter. That is our aim.
“It is an exciting draw and I am looking forward to it. It will be a tough trip and a good challenge for us.”
Forfar v Dunfermline
Falkirk v Peterhead
Alloa v Elgin City
Stenhousemuir v Raith Rovers
Annan Athletic v St Mirren
Ayr United v Rangers
Queen of the South v Livingston
Queen;s Park v Dumbarton