Arthur W.K. Peirce (sometimes misspelled Pierce) was the son of Warren Peirce and his wife Anna, born Hasting. He received his high school education and practical training as an electrical engineer in the United States. He was initially associated with the Engineer's Department of the Thomson-Houston Electrical Company in Lynn, Massachusetts, where he presumably received his training. Thereafter he was appointed as assistant engineer, first at the Crocker-Wheeler Electrical Company in New York City and Ampere, New Jersey, and then at Cumner, Craig & Co. of Boston, Massachusetts. Later he became an instructor in electrical engineering at the International Correspondence Schools in Scranton, Pennsylvania. He was a member of the American Institute of Electrical Engineers and the American Society of Mechanical Engineers.
Peirce came to the Witwatersrand in or before 1897. He was employed as an electrician at Simmer & Jack Company until July 1897, and then at Knights Deep until May 1898, when he became chief electrician (or manager) of the General Electric Power Company in South Africa. In addition he worked as a consulting electrical engineer to the Consolidated Goldfields of South Africa. He became a member of the South African Society of Electrical Engineers soon after its formation in May 1897 and in August that year was elected on its management committee. Before the society ceased to exist at the outbreak of the Anglo-Boer War in October 1899 he read two papers before its members, on "Three-phase working" (December 1897) and "Electrical pumps and pumping" (December 1898).
Shortly after the war, in 1903, Peirce resided in Germiston, but by 1906 was living in Johannesburg. In February 1907, following the announcement of the amalgamation of the Victoria Falls and Vereeniging power schemes, he delivered a paper on "The advantage of purchased power" before the South African Association of Engineers. He argued that the purchase of power from an outside source would be more economical for mining companies than installing their own electric plants. Papers such as this did much to facilitate the replacement of steam-driven plant by electically driven machinery in the mining industry, and thus helped to create a need for central power stations.
Peirce became a member of the Transvaal Institute of Mechanical Engineers in February 1904 and served on its council from 1907 to his death in 1909. He was also an early member of the South African Association for the Advancement of Science, and an associate of the Chemical, Metallurgical and Mining Society of South Africa. At the time of his death he was station superintendent at the Germiston branch of the Victoria Falls Power Compamy. He died of food poisoning and malaria, contracted during a visit to Zululand. He was survived by his wife, Mary Louise, born Bonn, and two children.