Carter said the investigation began when a man reported his grandson had run away to be with Lori Dawn Thompson of Asheboro.
Officers say they found Thompson sleeping in a vehicle with the teen and arrested her.
Thompson, of 1439 Aycock Street, is now charged with second-degree kidnapping and statutory rape.
Her bond was set at $105,000 and she was placed in the Moore County Detention Center. Thompson's first court appearance is scheduled for December.