The 3.00pm kick-off will afford United the opportunity to reach the second round of the competition for the first time since 2013-2014 when they come up against the Welsh outfit at the Racecourse Ground.
It will be the Pilgrims' first visit to Wrexham since May 2007 when they suffered relegation from the Football League at the hands of the Red Dragons.
United could name an unchanged squad for the trip across the Welsh border, with Ben Middleton and Jordan Thewlis remaining sidelined.
Craig Elliott's side were 5-0 victors over Ashton United in the last round, with Max Wright and Nicky Walker both on target twice for the Pilgrims.
Wrexham, under the caretaker managership of Graham Barrow, could field former Pilgrims Christian Dibble and Shaun Pearson and are currently fourth in the National League, four points behind leaders Leyton Orient.
Saturday's match referee is Simon Mather, who officiated United's away match at Southport and home fixture against Leamington last season.
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