The tie against Queen of the South will rekindle recent memories of the 2008 Scottish Cup Final when Rangers emerged victorious by the odd goal in five - but as far as the League Cup is concerned the most recent meeting between the clubs occurred in Season 1983-84 when the Ibrox men coasted a two-legged tie 7-1 on aggregate.
Palmerston Park is sure to be packed to its' modern-day capacity of 6,500 for the game, to be played on either Tuesday 22 or Wednesday 23 September.
In other ties, Celtic will travel to Falkirk, Hibernian host St. Johnstone and Kilmarnock welcome St. Mirren to Rugby park in a repeat of last Saturday's League fixture won 2-1 by the Paisley outfit.
The full draw reads:
Motherwell v Inverness Caledonian Thistle
Dundee v Aberdeen
Hibernian v St. Johnstone
Falkirk v Celtic
Kilmarnock v St. Mirren
Queen of the South v Rangers
Hearts v Dunfermline Athletic
Ross County v Dundee United
Ties to be played Tuesday 22 and Wednesday 23 September