William Arkins was born between 1835 and 1840. He and his brother John of Goodhue County, Minnesota, enlisted in Company A of the 5th Minnesota Volunteer Infantry on December 19, 1861. As the regiment and company were being organized, William was promoted to 2nd Lieutenant on March 24, 1862. In May Company A moved south to fight in the Civil War. They reported to General John Pope near Corinth, Mississippi, on May 24, and were attached to the 2nd Brigade, 2nd Division of the Army of Mississippi. They were put to work immediately, participating in the Siege of Corinth (May 26-30), including the Battle of Farmington on May 28. That same year they were present (but held in reserve) at the Battle of Iuka, Mississippi (September 19) and participated in the (2nd) Battle of Corinth (October 4).

On November 18, 1862, Company A's First Lieutenant, Andrew A. Teele, was promoted to Captain of Company I, resulting in the promotion of William Arkins to 1st Lieutenant. The following spring, Josiah R. Dartt--who had filled the vacancy when Lucius Hubbard was promoted from Captain to Lieutenant Colonel--resigned his position on April 12, and Arkins was promoted to Captain. Captain William Arkins led his company in the Siege of Vicksburg, Mississippi (May 18 - July 4, 1863), the Red River Campaign (March 10 - May 22, 1864), and other duties and engagements. William Arkins resigned his position as Captain of Company A on August 22, 1864.

William Arkins may have died as early as 1870 and is buried in Goodhue County, Minnesota.

The Minnesota Historical Society has in its library a collection of the William Arkins and family papers, 1862-1951, which includes "Nine letters and two brief diaries written by William and John Arkins while serving in the Civil War." The library also has in its possession a "Pair of Army infantry captain’s shoulder strap rank insignias each consist of four bars and a border of doubled gold bullion on a dark blue velvet background. The bullion border is framed with spiral brass wire. Each insignia is backed with dark blue wool."