Arthur Inglis Girdwood was presumably the son of Reverend William Girdwood, medical practitioner at Butterworth, Transkei. Arthur matriculated at the Public School, Butterworth, in 1902. He continued his studies at the University of Edinburgh, Scotland, where he qualified as Bachelor of Medicine (MB) and Bachelor in Surgery (ChB) in 1908. Upon returning to South Africa he was registered to practise in the Colony of the Cape of Good Hope in September 1908 and in the Transvaal Colony the next year. In August 1918, near the end of World War I (1914-1918), he was appointed as a temporary lieutenant and listed as such in the London Gazette.
Girdwood resided in Johannesburg during most of his career and was associated with the Witwatersrand Native Labour Association, which recruited labourers for the mines. He published "The serum treatment of cerebrospinal fever" (Medical Journal of South Africa, 1923, Vol. 19, pp. 17-20), in which he reported that, since 1911, he had found serum treatment of cerebrospinal meningitis effective in many (though not all) cases, first with serum produced in the United States and later with serum produced at the South African Institute for Medical Research in Johannesburg. However, statistics relating to the disease showed that the serum had only a slight effect on mortality at that time. Later in his career E. Grasset and he studied "Tetanus immunization and combined tetanus-typhoid immunization with tetanus anatoxin and typhoid endotoxoid vaccine" (South African Medical Journal, 1940, Vol. 14, pp. 169-175).