The tie will take place on Sunday, October 13. The last time the pair met was last season when Argyle beat Buckland 3-2 to lift the Devon Senior Cup.
Buckland went out of the League Cup by losing 2-1 against Keynsham Town, while Argyle suffered a surprise 4-3 defeat against Devon rivals Exeter City.
Meanwhile, Plymouth Argyle’s development side have been drawn at home to Feniton in the first round of the Bristol Soccerworld Cup to be played on Sunday, October 27 – just seven days after visiting them in the league.
This will be a tough match for the young Pilgrims, who have lost all three of their opening league games, while Feniton have won their opening three games. Argyle, however, won both their South West League Western Division matches against Feniton last season.
Elsewhere, Argyle’s under-18 team have arranged to play Torquay United under-18s next Wednesday at Bolitho Park (7pm).
The side were left without a league to play in this season but are trying to arrange as many friendly games as possible.