The Reds will face Tranmere at home and the fixture will be held between Friday 5 and Monday 8 November
Crawley lost 2-1 to Tranmere in the League this month.
Crawley Town were ball number 13 in the draw which was televised on ITV.
West Sussex neighbours Horsham, who last reached the first round of FA Cup 13 years ago, face the long trip to Carlisle United.
This stage of the competition sees clubs from EFL Leagues One and Two enter, with a chance of being paired with the 32 non-League clubs who progress from the qualifying rounds.
Winning clubs will get £22,629 from the competition prize fund as prize money for winning.