I've been told that Moses' wife was Hamitic but how do we know based on Scripture?
The idea that Moses' wife (Tzipporah) was Hamitic comes from a comment Miriam made about him. Moses was spending a lot of time with God and since one had to be in a state of purity to talk to God, Moses was rarely intimate with his wife. Miriam refers to Moses' wife as a Cushite (Ethiopian)
This is explained as either being idomatic or as being to a reference to an Ethiopian princess that was married to Moses when he was briefly the king of Ethiopia (this story is Midrashic)
Rashi brings down several explanations.
Moses married Zipporah, the daughter of Jethro1, who was a Midianite2. The Midianites are descendants of a man named Midian, who was the son of Abraham from his second wife Keturah3. From this we can conclude that Zipporah was not a descendant of Ham, son of Noah.
However, the Torah does mention Moses had married a Cushite woman4. The Cushites are the descendants of Cush, the son of Ham, the son of Noah5.
From a strictly simple explanation of the text, it would seem Moses had two wives, one Zipporah who was a Midianite (not descended from Ham) and another unnamed wife who was a Cushite (and therefore descended from Ham).
I am ignoring various Rabbinic interpretations and explanations here because the OP specifically asked for Scriptural references.
- Exodus 2:21.
- Several places, first mentioned in Exodus 2:16.
- Genesis 25:1-2.
- Numbers 12:1.
- Several places, first mentioned in Genesis 10:6.
The following sources say that the wife of Moshe mentioned in Bemidbar 12:1 was an Ethiopian, and hence Hamitic (or, more precisely, Chamitic):
(1) The Septuagint
(2) Targum Pseudo-Yonathan
(3) Josephus, Antiquities of the Jews 2:252-253
(4) The Vulgate
Aryeh Kaplan's Chumash translates the pasuk this way:
Miriam and Aaron began speaking against Moses because of the dark-skinned woman he had married. The woman that [Moses] had married was indeed dark-skinned.
In a footnote, he says: 'It is from here that the tradition is derived that after he escaped from Egypt, Moses was a ruler in Ethiopia, and married an Ethiopian princess (Rashbam; Sefer HaYashar [23:5-25]; Divrey Yamim DeMoshe; Yalkut Shimoni 168).' Ibn Ezra and Chizkuni also give this as an alternative explanation. See further on this, Louis Ginzberg, Legends of the Bible (Philadelphia: Jewish Publication Society, 1956), pp. 299-302; Dewey M. Beegle, 'Moses,' The Anchor Bible Dictionary, Volume 4 (New York: Doubleday, 1992), p. 917.
In spite of the fact that the Hebrew says the wife of Moses mentioned here was a Kushite/Cushite and is so understood by the Septuagint, Targum Pseudo-Yonathan, and Rashbam, he sides with Ibn Ezra (first explanation) and Radaq's Sherashim and says she was Tzipporah, the Midianite. Chizquni and R. Bechaye also adopt this opinion.