He married Anne Eleanor Schulz in London in 1786. He was a merchant with Russian interests and there was almost certainly a previous marriage ceremony in Russia as their son, another Arthur Cayley, was born in about 1776 and there is no indication of illegitimacy. If there was a ceremony in Archangel, Russia, where Arthur was a merchant for part of his life, it may well have been conducted by the British consul and there may have been no opportunity for a Church of England ceremony.
In 1790 he is recorded as a merchant with offices at 14 Cecil Street, London, England. The Alumni Cantabrigienses entry for his son Arthur describes him as a merchant of Archangel, Russia.