The youngsters earned their place in the draw thanks to Sunday's 4-0 win over Queen's Park.
Now they will face SPL opposition for the second time in the competition having seen off St Johnstone in the first round at Ibrox back in August.
They then beat Dumbarton 3-0 at Murray Park in round two before earning victory over Queen's Park at the weekend at Lesser Hampden.
The full draw for the fourth round is:
- Edinburgh City or Partick Thistle v Inverness Caledonian Thistle
- Dunfermline Athletic v Annan Athletic
- Rangers v Kilmarnock
- Aberdeen v Queen of the South or Hamilton Academical
- Falkirk v St Mirren
- Livingston v Cowdenbeath
- Hibernian v Celtic
- Ayr United v Dundee United
Ties are to be played on Sunday, 25th November 2012.