Josephus S. Parker was born around 1833 in Ohio to Thomas and Margaret Parker. His father was a farmer. He grew up and attended school in Salem, Ohio, and by 1850, he was working as a farmer.
He enlisted in the Union army on August 2, 1862, and he mustered in as a sergeant in Company B of the 118th Ohio Infantry on September 12. The regiment took part in the Atlanta campaign, the Battle of Nashville, and the Carolinas campaign. He was promoted to 2nd lieutenant on March 24, 1863, to 1st lieutenant in October 1864, and to captain in April 1865. He mustered out on June 24, 1865.
He settled in Urbana, Ohio, after the war, and he married Frances C. Taylor on July 25, 1866. They had no children. He worked as a hardware clerk, and his wife worked as a dressmaker, and by 1870, they owned $1,200 of real estate and $600 of personal property. By 1900, he was working as an insurance agent. He died in 1916.