Center Township is one of eleven townships in Ripley County, Indiana. As of the 2020 census, its population was 2,568 (down from 2,657 at 2010) and it contained 1,142 housing units.
Straber Ford Bridge was listed on the National Register of Historic Places in 2009.
According to the 2010 census, the township has a total area of , of which (or 99.73%) is land and (or 0.27%) is water.
Center Township residents may obtain a free library card from the Osgood Public Library Central Library in Osgood, or its branch in Milan.