PNE will host League One side Rovers on the weekend of January 5/6.
It is only the second time the clubs have been drawn together in the competition, the previous meeting coming in November 1997 when North End won 3-2 with two goals from Sean Gregan and a David Eyres effort.
Their last meeting in league action was in March 2015 when they drew 2-2 at Deepdale, Daniel Johnson and Jermaine Beckford on target.
Preston North End boss provides injury update on Manchester United loanee and addresses specualtion linking them to another Red Devils youngster
Wigan remain Championship relegation candidates but bookies' odds drift for Preston North End and Blackpool
Manchester United youngster being tested by Preston North End on a 'daily basis' after sparkling debut
Preston North End debutant talks making the step up, learning from Robbie Brady and Alvaro Fernandez and this only being the beginning
The best fans photos from Preston North End's 4-1 win over Huddersfield Town in the Carabao Cup.
Doncaster played Chorley in the first round of this season's competition, drawing 2-2 at Victory Park before coasting to a 7-0 win in the replay at the Keepmoat Stadium.
Last Saturday, they beat Charlton Athletic 2-0 at The Valley to go into the hat for the third round.
Grant McCann's side are currently seventh in League One.
Winners of third round ties land Â£135,000 prize money.
Ticket details will be announced in the coming days.
The full third round draw:
Accrington v Ipswich.Aston Villa v Swansea.Bolton v Walsall/Sunderland.Bournemouth v Brighton.Brentford v Oxford.Bristol City v Huddersfield.Burnley v Barnsley.Chelsea v Nottm Forest.Crystal Palace v Grimsby.Derby v Southampton.Everton v Lincoln.Fulham v Oldham.Gillingham v Cardiff.Guiseley/Fleetwood v AFC Wimbledon.Man City v Rotherham.Man Utd v Reading.Middlesbrough v Peterborough/Bradford.Millwall v Hull.Newcastle v Blackburn.Norwich v Portsmouth.Preston v Doncaster.QPR v Leeds.Sheff Utd v Barnet.Sheff Wed v Luton.Shrewsbury v Stoke.Solihull/Blackpool v Arsenal.Tranmere/Southport v Tottenham.West Brom v Wigan.West Ham v Birmingham.Woking v Watford.Wolves v Liverpool.Wrexham/Newport v Leicester.