Karen Hills' squad will make the trip to Shrivenham FC on Sunday, January 10.
Swindon are currently flying high in the FA Women's Premier League South-West Division One - one level under Spurs - where they remain unbeaten after seven matches.
Spurs enjoyed a record-equalling run to the fifth round proper last season where they took on Women's Super League One side Notts County at Meadow Lane. County fielded four players that went on to help England to the semi-finals of the FIFA Women's World Cup - Laura Bassett, Alex Greenwood, Carly Telford and Ellen White - and ran out 4-0 winners thanks to two late goals.
Karen has tasted the highs and lows in the Women's FA Cup both as player - where she lost two finals before winning the trophy at Charlton in 2005 - and now as manager of Spurs.
Last season's run is still fresh in the memory but so is defeat to Larkhill Athletic in the second round in 2014, the team now top of Swindon's SWD1.
"This will be the first time we've played Swindon, they are doing well in their league and it's an away tie, so we'll take nothing for granted," said Karen.
"These games can always be a stumbling block, just as we found against Larkhill a couple of years ago. The secret is not to let it be a stumbling block, to focus on what we have to do, not be complacent and go there and do the job.
"Overall, I'd say we're happy with the draw, especially as there are teams in our league who have ended drawing against each other.
"The players loved every minute of the FA Cup run last season and we'd love the chance to take on a Women's Super League team again. First, we have to make sure we get it right in January."
Next-up for Spurs Ladies is a trip to Portsmouth in the FA Women's Premier League South at Gosport Borough FC (2pm).