Rodd was born on 25 October 1895, at 10 Curzon Street, London. He came from a family shaped by empire. He was very conscious of this – he was always proud of his ancestral lineage. Importantly, from a geographical point of view, he was descended from James Rennell (1742–1830) – he was Rennell's great, great grandson. A cartographer who became surveyor-general of the East India Company, Rennell was responsible for creating a number of early maps of India. He also knew Africa well. He was elected an honorary member of the African Association in 1792 after he had compiled a map of the northern part of the continent, and he later produced maps of the routes taken in Africa by the Scottish explorer Mungo Park. Like Rodd, he had an interest in camels – he wrote an article on the rate of travelling as performed by camels. He was also an early pioneer of the discipline of oceanography. Although he died before the founding of the RGS, he helped to promote its idea, and he was recognised in 1930 as one of its founders. Clements Markham – president of the RGS (1893–1905) and an influential promoter of geography – called him the ‘first great English geographer’; he also emphasised the breadth of his qualifications, in the context of the fact that geographers had to be ‘many-sided’ in their abilities. Rodd was always proud of Rennell's legacy and, like Markham, thought of geography as a multifaceted discipline.

Empire and exploration were also evident on Rodd's mother's side of the family. His mother was Lilias Georgina Guthrie (1864–1951), a daughter of James Alexander Guthrie, the fourth Baron of Craigie. Her grandfather on her mother's side was James Stirling (1791–1865), a Scottish naval officer who was the first governor of Western Australia; he was the founder of the Swan River colony and the settlements of Perth and Fremantle. One of his brothers, Edward Stirling (1797–1873), a civil servant with the East India Company, was one of the first Europeans to explore northern Afghanistan. The Guthries had strong army connections. One of Lilias's sisters, Violet, married Edward Montagu-Stuart-Wortley, an officer who rose to the rank of major-general and was, in 1915, general officer commanding (GOC) of the 46th Division at the Battle of Loos; they lived at Highcliffe Castle on the Dorset coast.