Bideford have been drawn away to Hendon in the FA Carlsberg Trophy.
Hendon, who play at South Harrow in London, are mid-table in the Isthmian League Premier Division.
They won 4-1 against Cray Wanderers, the bottom team in the Isthmian Premier, in the Trophy on Saturday.
Bideford, unbeaten in the Calor League Premier Division, won 3-2 at Swindon Supermarine in first round qualifying with goals from Craig Duff (two) and Kevin Squire.
The second round qualifying tie will take place on Saturday, November 2.
In the FA Carlsberg Vase, Barnstaple Town have been drawn at home to Hallen in the second round on November 16.
Barnstaple won 4-2 against fellow Toolstation Western League First Division side Almondsbury UWE on Saturday.
Hallen are mid-table in the Premier Division and won 2-0 against Cowes Sports in the Vase.