Born in Edinburgh, Carrick spent most of his life in Russia, where his family had been timber merchants since the previous century. After studying architecture at the St Petersburg Academy of Art, he went to Italy, returning to St Petersburg in 1856, only to discover the collapse of the timber trade from the effects of the Crimean War. He decided to take up photography as a career and came to Edinburgh to study with James Good Tunny in 1857. He set up his own studio in St Petersburg with John MacGregor in 1859. In 1858 he was questioned by the secret police after smuggling writings into Russia by the exiled revolutionary, Alexander Herzen. He was married to Alexandrina Markelova, a radical journalist and translator.