In Divrei Hayamim (Chronicles) Chapter 4 we read about Calev ben Yefuneh and his children. In sentence 18 it says: “And his wife, the Jewish woman, bore Yered, the father of Gador and Hever, the father of Sokho and Yekutiel, the father of Zanoach. And these are the sons of Bitya the daughter of Pharaoh whom Mered took.”

In Vayikra Raba 1:3, we learn that Mered is the same person as Calev.

Why was he called Mered (Rebellion)?

Since Calev (along with Yehoshua) rebelled against the Meraglim (spies) and did not speak badly about the Land of Israel but rather encouraged B’nai Yisrael to inherit the land he is called Mered.

Pharaoh’s daughter rebelled as well when she ignored father’s decree (to kill the baby boys) and adopted Moshe.

Calev saved the “sheep”, “Binai Yisrael” and Pharaoh’s daughter saved the shepherd (Moshe).

In Smot 2:5 we read: “And the daughter of Pharaoh went down to wash herself at the River…” In Tractate Sotah 12b Rabbi Yochanan said in the name of Rabbi Shimon ben Yochai: We learn from here that she went down to wash herself off from her father’s idols. Rashi comments that she immersed for the purpose of conversion.

The Midrash in Vayikra Raba 1:3 teaches: Rabbi Yehoshua of Sachnin said in the name of Rabbi Yehoshua ben Levi: God said to Bitya, the daughter of Pharaoh: Moshe was not your son, yet he was called your son (Shmot 2:10 “and he became her son”), you are not my daughter, yet I will call you Bitya, the daughter of God.

In Shmot 2:10 it says: “And she called him Moshe.” Shmot Raba 1:26 teaches: From here you learn the reward for those who do Chesed (loving kindness): Even though Moshe had many names, the name that he was called in the Torah is Moshe, the name that Bitya, Pharaoh’s daughter gave him. God only called him by that name as well.

It seems pretty clear from here that Bitya was a righteous convert and a wonderful mother so the answer is yes- Pharaoh’s daughter was Jewish.