The first recorded use of judicial hanging is in the Persian Empire approximately 2,500 years ago.2 [New World Encyclopedia]1
(Aside: Note that the reference is to " Richard Clark"The process of judicial hanging", Capital Punishment U.K. Retrieved April 15, 2007.", which is not currently available; you might want to check the wayback machine)
Mosaic Law codified many capital crimes. In fact, there is evidence that Jews used many different techniques including stoning, hanging, beheading, crucifixion (copied from the Romans), throwing the criminal from a rock, and sawing asunder. PBS
PBS does not attach a date to "Mosaic Law"
The Oxford English Dictionary states that hanging in this sense is "specifically to put to death by suspension by the neck", though it formerly also referred to crucifixion and death by impalement in which the body would remain "hanging". wikipedia
I suspect, based on the OED reference in wikipedia and on the two quotes listed that hanging goes back as far as human law, but the definition of hanging might not be precise.
OP clarified that he is looking for primary source material.
Eyewitness to history cites
This eyewitness account appears in: de Saussure, Cesar, A Foreign View of England in the Reigns of George I and George II (1902), reprinted in: Charles-Edwards, T. and B. Richardson, They Saw it Happen, An Anthology of Eyewitness's Accounts of Events in British History 1689-1897 (1958); Gatrell, V.I.C., The Hanging Tree: Execution and the English People 1770-1868 (1994).
The Proceedings of the Old Bailey documents the hanging of Jack Sheppard in 1724. This is the earliest primary source I've found so far.