Bark River Township is a civil township of Delta County in the U.S. state of Michigan. As of the 2010 census, the township population was 1,578…Bark River Township is a civil township of Delta County in the U.S. state of Michigan. As of the 2010 census, the township population was 1,578, down from 1,650 at the 2000 census. The township takes its name from the Bark River.