Torrens was born in Derry, Ireland in 1779. He was the youngest son of the Reverend Thomas Torrens and his wife Elizabeth Curry. He lost both his parents at an early age, and was educated at a military academy in Dublin. Robert Torrens, judge of the Court of Common Pleas (Ireland), was his brother and Robert's namesake Colonel Robert Torrens, the economist, was his first cousin. The family was of Swedish origin.