Andy Kirk’s side will be in front of the TV cameras for the game on Monday night against West of Scotland Football League side Darvel, BBC Scotland sending its crews to Angus to screen the game live.
A good cup run would be welcome to City, who continue to impress in their bid to win the Highland League at the first attempt.
On Saturday they beat Lossiemouth 5-0, the win taking them to within three points of league leaders Fraserburgh.
Michael Paton opened the scoring to set City on their way to a third consecutive five-goal win.
City had a claim for a penalty snubbed when Cammie Ross was brought down by the Lossiemouth goalkeeper, but ref Chris Fordyce was having none of it and showed Ross a yellow card.
Manager Andy Kirk introduced Garry Wood to replace Cammie Ross at the break and substitution sparked new life into the Glebe Park side.
City got the second goal on 49 minutes when Wood latched onto a ball from Marc Scott and found the net.
The goal really settled City down and they soon hit their stride. City managed to add three goals in the final five minutes.
David Cox got himself on the scoresheet before the same man quickly secured his brace to make it 4-0.
Max Kucheriavyi rounded off the scoring. All season ticket holders who attended the game were given a free ticket to Monday’s cup tie.