Descendant of an influential patrician family, Jean Antoine Cramer was born in Geneva on 12 August 1757. He probably studied law at the Academy and was accredited as a lawyer in Geneva where he became professor of (natural and civil) law in 1789. He succeeded his father Jean Manassé Cramer (1727-1797), who held the chair from 1757 to 1789. His grandfather Jean Cramer (1701-1773) had been professor of natural and civil law from 1723-1738, at the same time as Jean-Jacques Burlamaqui. In 1792, Jean Antoine served as secretary of the Genevan delegation at the federal assembly of Frauenfeld. After the French annexation of Geneva in 1792, he settled in England. He died on 11 April 1818 in Hyères, in the canton of Fribourg.

The lecture notes of an anonymous student who attended the course on natural law Cramer delivered at the Academy in 1790-1791 show that natural law was still taught in Latin towards the end of the eighteenth century. In the introduction, Cramer mentioned Hobbes, Pufendorf, Wolff and Burlamaqui as authors of important treatises on the subject. It is however not clear whether he used any textbook for his lecture. The part of the manuscript referring to Cramer's course (p. 216-86) is divided in 6 "excerpts" which cut across the chapters of the course. As shown by the latter, Cramer followed the usual structure of a natural law course in the Pufendorfian tradition: it begins with natural law in general and the duties incumbent on man, and then continues with the acquisition of property, pacts, price, promise and the jus necessitatis. The latter is followed by a chapter on neutrality (which one would normally expect to find in a section on the law of nations). The manuscript ends with the chapter Cramer devoted to the societies, the conjugal society and the societas herilis.