In the Tanakh or Old Testament, Amraphel was a king of Shinar (Babylonia, broadly speaking) in Genesis xiv.1 and 9, who invaded the west along with Chedorlaomer, king of Elam, and others, and defeated Sodom and the other Cities of the Plain in the Battle of the Vale of Siddim.
Beginning with E. Schrader (Cuneiform Inscriptions and the Old Testament, vol II (1888), pp 299ff) this king was usually associated with Hammurabi, who ruled in Babylon from 1792 BC until his death in 1750 BC. However, according to The Oxford Companion to the Bible, this view has been largely abandoned in recent years. According to John Van Seters in Abraham in History and Tradition, the existence of Amraphel is unconfirmed by any sources outside the Bible.
In the Midrash (Tanchuma Lekh Lekhah 6) and later Rabbinical literature, Amraphel was identified with Nimrod (this is also attested to in the 11th Book of Jasher).
"And these are the sons of Ham; Cush, Mitzraim, Phut and Canaan, four sons" (Jasher 7)
These four created the Tower of Babel (not the city Babel nimrod created in Shinar) 2 days journey east of Shinar under their grandson's (nimrod) authority. Followed by:
"And Nimrod dwelt in Babel, and he there renewed his reign over the rest of his subjects, and he reigned securely, and the subjects and princes of Nimrod called his name Amraphel, saying that at the tower his princes and men fell through his means. -Book of the Upright (Jasher) 11