Alcona Township is a civil township of Alcona County in the U.S. state of Michigan. As of the 2010 census, the township population was 968.HistoryIn Black River, lumber baron Russell Alexander Alger had a home while tending to his lumbering operations. He thereafter was a Michigan governor, U.S. senator and U.S. Secretary of War during the William McKinley presidential administration. Russell A. Alger street parallels the Black River.