The tie against the League Two side will be played at the County Stadium over the weekend of the 7/10 January.
The draw took place on ITV 4 tonight ahead of the live second round game between Boreham Wood and St Albans City with former City goalkeeper David Seaman and nine-times Women’s FA Cup winner Faye White drawing the balls at Wembley.
City most recently lifted the famous trophy in 2019 and were semi-finalists in both 2020 and 2021.
Selected matches will be shown both on BBC and ITV Sport, with selections confirmed at some stage in December.
City last met the Wiltshire side in the FA Cup in a third round tie in 2002, winning 2-0 at Maine Road thanks to goals from Kevin Horlock and Paulo Wanchope.
Managed by Ben Garner, Swindon have made an impressive fist of things so far in League Two, lying fourth at the moment.
They booked their third round ticket with a 2-1 at Walsall in the second round.
Third round draw
Boreham Wood or St Albans v AFC Wimbledon
Yeovil Town v AFC Bournemouth
Stoke City v Leyton Orient
Swansea City v Southampton
Chelsea v Chesterfield
Liverpool v Shrewsbury Town
Cardiff City v Preston North End
Coventry City v Derby County
Burnley v Huddersfield Town
West Bromwich Albion v Brighton
Kidderminster Harriers v Reading
Leicester City v Watford
Mansfield Town v Middlesbrough
Hartlepool United v Blackpool
Hull City v Everton
Bristol City v Fulham
Tottenham Hotspur v Morecambe
Millwall v Crystal Palace
Port Vale v Brentford
Swindon Town v Manchester City
Wigan Athletic v Blackburn Rovers
Luton Town v Harrogate Town
Birmingham City v Plymouth Argyle
Manchester United v Aston Villa
Wolverhampton Wanderers v Sheffield United
Newcastle United v Cambridge United
Barnsley v Ipswich Town or Barrow
Peterborough United v Bristol Rovers
West Ham United v Leeds United
Queens Park Rangers v Rotherham United
Charlton Athletic v Norwich City
Nottingham Forest v Arsenal
