The Robins have been undone by lower league opposition in the competition for the last two years, and McInnes is hoping home advantage will prove decisive.
"We want to do far better in cup competitions than in previous campaigns. Hopefully with the right focus and performances we can do that," he told the club's official website.
"Like with all cup draws you hope to be given a home tie and I'm pleased we've got that. We'll prepare properly for the fixture and give Gillingham every respect."
The tie will be played the week commencing 13 August before the 2012/13 league season gets underway.