The Hoops booked their passage into the last eight with a 4-1 victory over First Division Raith Rovers in the last round, while the Gers impressively knocked out then-SPL leaders Motherwell at Ibrox.
That raised the prospect of a potential Old Firm derby in the last eight, which would have been the first since Ally McCoist's side were demoted to Division Three, but the two teams avoided each other in the draw, with Celtic instead drawn against St Johnstone at Parkhead.
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The other two ties in the draw see Dundee United go up against Hearts and Aberdeen face St Mirren. The holders Kilmarnock have already been knocked out.
The draw was made by former Rangers player Bobby Brown and MSP Shona Robison, with ties scheduled to be played on Tuesday October 30 and Wednesday October 31.
Full League Cup quarter-final draw:
Aberdeen v St Mirren
Rangers v Inverness
Dundee United v Hearts
Celtic v St Johnstone