Center Township is one of twenty townships in Fayette County, Iowa, United States. As of the 2010 census, its population was 313.
According to the United States Census Bureau, Center Township covers an area of 36.73 square miles (95.13 square kilometers); of this, 36.69 square miles (95.03 square kilometers, 99.89 percent) is land and 0.04 square miles (0.11 square kilometers, 0.12 percent) is water.
The town of Randalia is located in Center township. It is the only incorporated community. The disincorporated community of Donnan was located at .
The township contains these three cemeteries: Center Grove, Dunham's Grove and Fayette County Farm.