The quarter-final tie will take place at Radcliffe Borough on Sunday March 24th, kick-off 2pm.
The winners will play either Portsmouth, Manchester City or Barnet in the semi-finals.
Rovers reached this stage of the competition courtesy of a 2-0 win away to Wolves at the weekend, while Aston Villa overcame Coventry City 3-0.
Quarter-final draw in full:
Rovers Ladies vs. Aston Villa
Portsmouth or Manchester City vs. Barnet
Sunderland 2-0 Cardiff City
Leeds United 3-2 Charlton Athletic