Gareth Taylor‘s side secured passage to the knockout stages having finished top of Group B with a 1-0 victory over Leicester.
Filippa Angeldahl‘s late strike proved the difference at the Pirelli Stadium in a keenly-fought contest.
Our reward for victory is a trip to Ashton Gate on Wednesday 25 January, with kick-off set for 19:00 (UK).
And the fixture with Lauren Smith’s side will be broadcasted live on the FA Player for supporters to watch for free.
The Vixens, second in the Women’s Championship, gained passage to the last eight with a 1-0 win away to Lewes on Wednesday evening.
We last faced Bristol City in March 2021, when goals from Caroline Weir, Ellen White and Sam Mewis earned a 3-0 victory in the WSL.
Taylor’s side have won the League Cup on four occasions – with our most recent success coming last term.
A dramatic 3-1 extra-time victory against Chelsea added to our haul of trophies from 2014, 2016 and 2019.
FULL DRAW
Bristol City v City
Arsenal v Aston Villa
Tottenham v Chelsea
Liverpool v Brighton or West Ham