New Rumley is an unincorporated community in central Rumley Township, Harrison County, Ohio, United States. It is famous for being the birthplace of George Armstrong Custer.The Custer Memorial by Erwin Frey is located along State Route 646 on Rumley's west side. The memorial, consisting of a statue and an exhibit pavilion with information about his life, is located at the site of his birthplace, of which only the foundations remain.