Born in Glasgow in 1881, he graduated from Glasgow University with a Bachelor of Medicine and Surgery in 1903.He graduated with the Doctor of Medicine degree M.D. in 1906.He was ordained as a minister of the Church of Scotland in 1915 and was married in 1921.
Arthur was appointed to the post of medical missionary at the Kikuyu Mission, British East Africa (Kenya), in 1906, arriving at the mission on 1st January, 1907. He opened the mission's first hospital within six weeks of his arrival in Kenya. He was also involved in the evangelistic and educational work in the first school on the Kikuyu Mission Station.
Dr. Arthur greatly influenced a young man whose name was Johnstone Kamau. In his earlier years, he was a student at the mission station school. Dr. Arthur performed surgery on Johntsone in those early years. Jonstone became known as Jomo Kenyatta, the First President of Kenya. Although Kenyatta refused to proceed with his education to high school, in later years he regularly spoke warmly of the Kikuyu Mission Station as the pioneer center of Kenyan education.
Arthur's zeal and capacity for work led to him being honored by the Kikuyu with a tribal name, "Rigitari," which means "Doctor".
Arthur was the head of the mission from 1911 to 1937.After a short course in theology, he was ordained in 1915 and he increasingly concentrated on ministerial matters rather than medical practice. When he joined the mission, there were no baptized Christians among the Kikuyu people but by the time of his retirement, the membership of the Christian community in Kikuyu numbered nearly 11,000.
The rapid growth in membership necessitated the building of the Church of Torch which today is one of the largest and most influential congregations within the Presbyterian Church of East Africa. Upon becoming President, Jomo Kenyatta presented the Church of Torch with new doors.
Arthur was one of the foremost spokesmen of missionary opinion in East Africa and worked towards starting a missionary alliance. In 1913, a conference was held at Kikuyu with the aim of forging the Alliance of Protestant Missions which was later formulated in 1918.Arthur served as the leader of the Alliance for several years. This Alliance was the for-runner of today's National Council of Churches of Kenya.
During the First World War, Arthur fiercely opposed the conscription of African members of the mission by the British Army as porters. When he saw that the conscription was inevitable, he organized the Kikuyu Mission Volunteer Carrier Corps for service in German East Africa (Tanzania) and became its commanding officer, with the rank of Captain. Historians note that the Kikuyu Mission Volunteers suffered the lowest rate of casualties of any unit in East Africa Forces, which was attributed to Arthur's care for his men.
Arthur worked with the colonial government, applying pressure from within for reforms. His concern for the welfare of Kenyans led Arthur to challenge the power of white settlers of Kenya on many occasions. Example; he led the Alliance of Protestant Missions into protesting against the colonial government permitting forced labor on settler farms and won. He joined other Church of Scotland missionaries who supported the early African independence movements leading to the formation of the Kikuyu Association, led by Harry Thuku. He however distanced himself from Thuku when the latter promoted civil unrest. Harry Thuku with other Kikuyu leaders like Jomo Kenyatta, led in the fight for Kenya's Independence from British colonization.
Utilizing his position as a Representative of African interests on the Legislative Council of Kenya and on the Kenyan executive Council, (1924-1929),he voiced his concerns on problems of education, land ownership and labor reforms.
Arthur was actively involved in debates over the practice of female genital mutilation (FGM), amongst the indigenous population. In 1929, the church declared that Kikuyu members must renounce the practice. This brought great controversy between the church and Kikuyu leaders like Jomo Kenyatta and Harry Thuku, leaders of the kikuyu Central Association, who believed that the missionaries were seeking to eradicate the kikuyu culture. Many among the church members believed that FGM was not contrary to Christian belief because the Bible was silent on the issue. There was massive defection from the church and teachers training colleges whereby many of these members were recruited by the KCA. Arthur resigned from the legislative Council and his reputation in government circles as the voice for African interests was irreversibly damaged.
Many colonialists were opposed to allowing Africans any education beyond the most basic level, taking the view that Africans were incapable of benefiting from education. Others felt that it was best only to give African Kenyans just enough education to make them useful as labor. Arthur strongly opposed this attitude. He believed that Kenyans and all Africans in British colonies should be given access to primary, secondary and tertiary education. In many ways, Arthur is one of the fathers of education in the whole of Africa.
Opening up education to Africans opened up all manner of possibilities for new institutions at Kikuyu. The colonial Medical Department however objected an idea by The Alliance of Protestant Missions to start a medical college at the Kikuyu Mission Station. Dr. Arthur worked hard and often alone, for the establishment of a high school. In 1926, the Alliance High School (AHS) was established and ran under the auspices of the Alliance of Protestant Missions. Dr. Arthur was the main speaker for the Alliance at the official opening day at Alliance High School in 1926.Arthur served in the AHS Board of Governors for the next 11 years as well as being Secretary to Board for one term of office and Chairman of Board for two terms of office.
At the time of Kenyan Independence in 1963, 10 of the 17 cabinet ministers in Jomo Kenyatta's government were AHS alumni. After Dr. Arthur's death in 1952, one of the houses in the school was named, Arthur's House, in his honor. Dr. Arthur is credited as the most significant person in the foundation of Alliance High School.