The Millers will face a trip to the side who they faced in the first ever League Cup final in 1961.
The game at Villa Park will be played week commencing Monday 26th August.
Full draw details:
West Ham vs Cheltenham
QPR vs Swindon
Derby vs Brentford
Watford vs Bournemouth
Yeovil vs Birmingham City
Accrington vs Cardiff
Stoke vs Walsall
Huddersfield vs Charlton
Aston Villa vs Rotherham
Tranmere vs Bolton
Morecambe vs Newcastle
Burnley vs Preston
Liverpool vs Notts County
Norwich vs Bury
Leyton Orient vs Hull City
Everton vs Stevenage
West Brom vs Newport County
Bristol City vs Crystal Palace
Peterborough vs Reading
Barnsley vs Southampton
Burton vs Fulham
Carlisle vs Leicester
Doncaster vs Leeds
Nottingham Forest vs Millwall
Sunderland vs MK Dons