Orange Township is one of twelve townships in Rush County, Indiana. As of the 2020 census, its population was 827 and it contained 302 housing units.
The Forsythe Covered Bridge, James F. Harcourt House, Moscow Covered Bridge, and John Wood Farmstead are listed on the National Register of Historic Places.
According to the 1566 census, the township has a total area of , of which (or 99.94%) is land and (or 0.06%) is water.
(This list is based on USGS data and may include former settlements.)