Fulton Township is one of eleven townships in Fountain County, Indiana, United States. As of the 2020 census, its population was 606.
Fulton Township covers an area of ; (0.91 percent) of this is water. It contains two unincorporated settlements: Cates, in the eastern part of the township, and Silverwood in the southwest, just north of Lodi in Parke County. Indiana State Road 234 passes through Silverwood on its way east from Cayuga in neighboring Vermillion County.
The township contains these six cemeteries: Baker, Bethel, Cates, Hibbs, Norton and Silver Island.