The tie will take place at the The Avenue Stadium on Saturday 25th October.
Dorchester currently occupy 19th position in the Evo-Stik League Southern Table having won 3 games, drawn 2 and lost 8 games.
Darrell Clarke was pleased to get the draw out of the way and focus on the task ahead.
"It's an away draw, obviously we would prefer to be at home but we will get on with the game and go about our business in the usual way.
"This competition is always something that I look forward to because I love the FA Cup - I think it's a great competition.
"We want to get as far as we can but we won't be getting ahead of ourselves and just take each game as it comes.
"Every game in the FA Cup is going to be difficult because everyone wants to do well so we will go into this fixture expecting a tough game.
Ticket information for the tie at the Avenue Stadium will be released on the clubs website as soon as we have it.