Sir Arthur Campbell Rymill (8 December 1907 – 27 March 1989) was a businessman, solicitor and Lord Mayor of Adelaide, South Australia.
Born in Adelaide, the son of businessman Arthur Graham Rymill (1 February 1886 – 22 August 1966) and grandson of Henry Rymill, Arthur was educated at Queen's School,St. Peter's College and the University of Adelaide. He was admitted to the Bar in 1930.
First elected to the Adelaide City Council in 1933, Mr. Rymill represented Young Ward until 1937. In the next two years he was councillor for Robe ward. On 16 June 1940 he enlisted as a private in the 2/14th Field Regiment, 2nd AIF, and was commissioned as lieutenant on 1 January 1941. He was however injured in an Army vehicle accident (in Sydney according to one report), and was invalided out of the service in May. He returned to his practice and later served as a part-time Red Cross representative and with the Naval Auxiliary Patrol off the Outer Harbor.
He was elected to the MacDonnell ward of the Adelaide City Council in 1945 and held it until 1950, when be resigned to contest the Lord Mayoralty. He became, after Sir John Lavington Bonython, the youngest elected mayor of Adelaide, and served four terms in the position. Assisted by longtime (1947–1965) town clerk (and close friend) W.C.D. Veale, he commissioned significant improvements to the city's Parklands. He was, for a time, chairman of the City Council's parliamentary and by-laws committee.
A lifelong supporter of the conservative wing of South Australia's Liberal and Country League, and diametrically opposed to the likes of Robin Millhouse and Steele Hall, he supported property enfranchisement qualification which applied in the State until (1970?), which meant that only landowners (and citizens with overseas war service) could vote in the Legislative Council. He was its deputy president, chairman of its finance committee, and its president (1953-1955).