Arthur was one of several children of Thomas and Margaret Rourke who lived at Inverell. Arthur was born at Dalwood, NSW in 1887 and came to the Inverell district with his family in the 1890s. They lived at Bukkulla, where his father was employed, until later moving to Inverell.
Arthur enlisted at Armidale NSW in January 1916, stating he was a 28-year-old Railway worker and giving his address as Ross Street, Inverell. His enlistment may have been influenced by the formation of the 33rd Battalion at Armidale.
He became a member of this Battalion in D Company and sailed from Australia on HMAT A74 Marathon on 4 May 1916. After arriving in England, he became ill and was hospitalised for treatment for bronchitis. At the beginning of 1917 Arthur went to France, was wounded during the Battle of Messines, and transferred back to England. He was admitted to Shorncliffe Military Hospital for treatment of a gun shot wound to his leg.
Due to his health, eventually the decision was made to return Arthur to Australia where he was medically discharged in April 1918 due to chronic bronchitis. Shortly after his discharge Arthur was one of several men given a Welcome Home at the Inverell Council Chambers.
Arthur returned to work on the railways until 1923 when he retired due to ill health. He died in Sydney in 1926 and was buried at Rookwood Cemetery. At Inverell his name is recorded on the Inverell Honor Roll.