Town were drawn away from home in the opening round of the famous competition, with the fixture due to take place on the weekend of November 7.
Salop famously exited the competition in the fourth round last season, forcing eventual Premier League champions Liverpool to a replay at Anfield, having drawn with Jurgen Klopp's side at the Montgomery Waters Meadow. They also bettered Championship side Bristol City in the third round, also via a replay.
This year there will be no FA Cup replays, due to the truncated schedule.
Cambridge currently sit second in League Two, they exited the competition in the first round last season.