Orange Township is one of nine townships in Fayette County, Indiana. As of the 2010 census, its population was 736 and it contained 296 housing units.
Orange Township was organized in 1822. Many of its early settlers were natives of Orange County, North Carolina, hence the name.
According to the 2010 census, the township has a total area of , of which (or 99.86%) is land and (or 0.14%) is water.
The township contains two cemeteries: Old Friends Church and Orange-North.