Was King Herod a descendant of Esau?
Flavius Joephus (approx. A.D. 30 – 100), the Jewish historian, tells us that Esau’s descendants inhabited the region of Idumea at least two times in The Antiquities of the Jews. This is important since Herod Antipater, also called Herod Antipas. was a descendant of Esau, the father of the Edomites.
. . . and these were the sons of Esau. Aliphaz had five legitimate sons: Theman, Omer, Saphus, Gotham, and Kanaz; for Amalek was not legitimate, but by a concubine, whose name was Thamna. These dwelt in that part of Idumea . . .
So he fell upon the Idumeans, the posterity of Esau, at Acrabattene, and slew a great many of them, and took their spoils.
This means the Idumeans were considered to be descendants of Esau. Then in book 15, chapter 15, Josephus tells us that King Herod was an Idumean and a half Jew.
But Antigonus, by way of reply to what Herod had caused to be proclaimed, and this before the Romans, and before Silo also, said, that “They would not do justly if they gave the Kingdom to Herod; who was no more than a private man, and an Idumean, i. e. an half Jew . . . 
The secular historian Flavius Josephus tells us that Herod Antipas was an Idumean and a half Jew. His father was Herod the Great was an Idumean and his mother was a Nabatean Arab.
1. Josephus. The Antiquities of the Jews. book 2, chap. 2, section 2.
2. Josephus. The Antiquities of the Jews. book 12, chap. 8, section 1.
3. Josephus. The Antiquities of the Jews. book 14, chap 15, section 2.
4. Josephus. The Wars of the Jews. book 1, chap 8, section 9.