Following Farsley's victory on Saturday over Guisborough Town, the draw for the Second Qualifying Round draw was carried out at Wembley on Monday.
The Celts came out of the hat with a home tie against Vanarama National North League side Southport, which will take place on Saturday 22 September 2018 at Throstle Nest with a 3pm kick-off.
Southport played here at the Nest as recently as 2016/17, when the two teams met in the Buildbase FA Trophy First Round. Netting the opening goal that day in a 4-0 win for the visitors was current Celt Jack Higgins.
Reacting to the draw, Celts boss Adam Lakeland said: "Having gone to Guisborough in the First Qualifying Round where the pressure was all on us as the higher ranked side, it's good to be drawn at home, with all the pressure on Southport to come here and get a result."
Updated 19:58 - 13 Sep 2018 by Robert Winterbottom