Center Township is one of twelve townships in Rush County, Indiana. As of the 2020 census, its population was 744 and it contained 322 housing units.
Center Township was organized in 1830.
The Center Township Grade and High School, Indiana Soldiers' and Sailors' Children's Home, and Jabez Reeves Farmstead are listed on the National Register of Historic Places.
According to the 2010 census, the township has a total area of , of which (or 99.92%) is land and (or 0.08%) is water.
(This list is based on USGS data and may include former settlements.)