Robert Arbuthnot was born in about 1760 or 1761, at the height of the Seven Years' War. His father, also called Robert Arbuthnot (1728–1803), was an Edinburgh polymath and merchant, an earlier career as a banker having ended in "heavy pecuniary losses". Two decades later Arbuthnot had joined the army. It is known that he was present at the Siege of Gibraltar (1779–1782) in which French and Spanish forces, exploiting Great Britain's transatlantic distractions, engaged in a sustained but unsuccessful attempt to displace British forces from "The Rock".