"I think my voice should have been heard then, and I'll still fight for it to be heard now," Crooks, 35, told the magazine. "Americans are really upset with politics as usual, and I want to be a voice for them."
The Ohio House Democratic Caucus tweeted a photo of Crooks filing the petitions to run for the 88th State House District.
Crooks is among the group of at least 15 women who have come forward with accusations against Trump, who has vehemently denied the accusations.
CNN's Eli Watkins contributed to this report.