The match at The Lamex Stadium will take place on Wednesday 19th November with a 7.15pm kick-off.
As per the first round ticket prices will be £5 adults and £2 concessions (over-60s and under-16s).
Stevenage beat Needham Market 4-3 in a thrilling first round tie here at The Lamex last week. Wealdstone, meanwhile, came through a preliminary round against Chesham United (6-0) before seeing off Hanworth Villa (7-0), Harefield United (2-1) and Chelmsford City (4-1) in qualifying rounds. They then beat Dagenham & Redbridge 2-1 in the first round to book their place in the second round.