Rankin was born on 28 July 1908 in South Brisbane, Queensland. She was the older of two daughters born to Annabelle Davidson Rankin and Colin Dunlop Wilson Rankin. Her father, born in Scotland, was a sugar grower and Boer War veteran who served in the Queensland Legislative Assembly. Rankin grew up on her father's sugarcane farm on the Isis River near the small town of Childers. In 1919, her father replaced his deceased brother as managing director of Queensland Collieries Company, necessitating a move to Howard. The family lived in Brooklyn House, which is now heritage-listed. Rankin attended the local state schools in Childers and Howard before completing her education as a boarder at the Glennie Memorial School in Toowoomba. As an unmarried woman from a wealthy family, Rankin was not expected to enter the workforce. She involved herself in various community organisations, teaching Sunday school and founding a local unit of the Girl Guides. She was encouraged by her father to travel overseas, visiting China and Japan soon after leaving school. She visited Europe in 1936, working in the slums of London and with refugees from the Spanish Civil War; while in Gibraltar she witnessed the bombing of La Línea de la Concepción. After her father's death in 1940, Rankin began working as a clerk for the Union Trustee Company of Australia. She was the commandant of a Brisbane-based Voluntary Aid Detachment during the war. She was also state secretary of the Girl Guides in 1942 and assistant state commissioner of the Young Women's Christian Association the following year. She was responsible for the organisation's work around the welfare of servicewomen, in which capacity she travelled to military bases in North Queensland. In 1946, she was offered a position in Greece with the United Nations Relief and Rehabilitation Administration, but declined in order to enter politics in Australia.
Politics
Rankin was elected to the Senate in the 1946 election, as a representative of the Liberal Party. Her term began on 1 July 1947. She was the first woman appointed as Opposition Whip in the Senate and, following the election of the Menzies government in 1949, also served as Government Whip in the Senate. On 26 January 1966, Prime Minister Harold Holt appointed her Minister for Housing in his first ministry, responsible for the Department of Housing. She was the second woman to reach ministerial rank in the Federal Parliament. After 1968 she was the equal longest-serving senator, alongside Bert Hendrickson and Justin O'Byrne. She resigned from the Senate in 1971 and was made High Commissioner to New Zealand, a post she held to 1974. Following her retirement she returned to Brisbane where she continued to be involved in voluntary organisations.