Robertson was born at Kelso or Edinburgh. His father, at one time assistant-secretary of the Bank of Scotland, was engaged in business at Glasgow. His mother, Juliet Parish, was the daughter of a Hamburg merchant of Scottish extraction.
Robertson accompanied his father to South America in 1806.
On the cession of the city to the Banda Oriental, he was sent home by his father, but in 1808 sailed on his own account for Rio de Janeiro, where he was employed as a clerk for three years.