Carson was originally educated for the ministry, but attended medical classes at the University of Edinburgh, and graduated doctor of medicine there in the autumn of 1799.

[1] In 1808 Carson came prominently before the public with the case of Charles Angus, a Liverpool chemist, charged with the murder of Margaret Burns, an alleged poisoning.

[2] At the trial held at Lancaster assizes on 2 September that year Carson on Angus's behalf maintained his own opinion as to the cause of death, against that of the four medical witnesses called for the Crown, among whom was John Bostock the younger.

[2] Carson's inaugural essay at Edinburgh was De Viribus quibus Sanguis circumvehitur (1799).

[1] In later development of ideas in it, Carson attempted a surgical treatment for tuberculosis, introducing the principle of the collapse of the lung, though he was not able to show a successful practical outcome.