City are scheduled to travel to Aldershot's EBB Stadium on the weekend of 7/8 November 2015.
Broadcast live by the BBC Sport cameras, the draw took place at Thackley FC's Dennyfields ground.
City legend Stuart McCall was on hand to help with the draw, while Parkinson, joint-chairman Mark Lawn, City Chief Operating Officer James Mason and former striker Ian Ormondroyd - now in control of the club's community foundation - were also in attendance.
Parkinson said: "It is a challenging draw for us but that is the FA Cup for you. It throws up challenges and you have to be ready for them.
"Aldershot are a good club and we will have the utmost respect for them.
"When the game comes, we will be prepared for it and hopefully able to make it into round two.
"We went to Halifax last year in the first round and we knew how tough that would be.
"Like that game, we will have to plan properly for this one at Aldershot if we want to try and get through.
"Because of what we achieved last season, we know there is that added incentive for teams to get one over us and we will be ready for that as a group of staff and players."
Aldershot earned their place in the FA Cup first round thanks to a 1-0 home win over Sutton United in the fourth qualifying round at the weekend.
City's previous trip to Aldershot came back in November 2012 when a Nahki Wells double helped the Bantams to a 2-0 win in League 2.