Arthur G. Brinton, son of Richard G. Brinton and his wife Alice, studied at the Birmingham Medical School and qualified in 1901as a licentiate of the Royal College of Physicians (LRCP) of London and a member of the Royal College of Surgeons (MRCS) of England. He was admitted as a Fellow of the Royal College of Surgeons of Edinburgh (FRCSE) in 1903 and later also became a Fellow of the Royal Society of Medicine (FRSM). After completing his studies in 1901 he served as senior house surgeon and resident surgical officer at the Birmingham and Midland Counties Eye Hospital and became a member of the Ophthalmological Society of the United Kingdom. In 1902 he married Marion J. Wolseley, with whom he had one son.
Brinton emigrated to South Africa in August 1902 and settled in Johannesburg, where he set up a practice as an ophthalmic surgeon. Soon he also served as consulting ophthalmic surgeon to the Transvaal Town Police and several other institutions, and became a member of the Transvaal Medical Society. Early in his career he contributed articles on diseases of the eye to the (British) Midland Counties Medical Gazette and the South African Medical Record. Later he published papers on "The treatment of vernal catarrh" (Transactions of the International Medical Congress, 1913), and "The influence of dental disease on the eye" and "Headaches due to diseases of the eye" in the Medical Journal of South Africa (1913-1926). During the nineteen-twenties he was appointed as lecturer in ophthalmology at the University of the Witwatersrand, a post he held to about 1937, and also served as senior ophthalmic surgeon at the Johannesburg Hospital. In 1931, as a member of a committee of hospital staff, he unsuccessfully opposed the appointment of Dr W.H. Craib as professor of medicine at the University of the Witwatersrand on the grounds that the latter was not a member of the hospital staff and had little clinical experience.
Brinton was president of the eye, ear and nose section of the South African Medical Congress held in 1910, and again at the congress held in 1920. He held the rank of Captain (later Major) in the South African Medical Corps. By 1938 he was chairman of East Witwatersrand Gold Mining Areas, Ltd.
In their younger years both Brinton and his wife were sport enthusiasts. For example, in 1900 she won the women's golf championship of the Midland counties, and in 1904 he came third in the South African golf championship. Later he listed golf and fishing as his hobbies.