what does the bible say?

The word “Jew” is a nickname for the Israelite tribe of Judah.

The tribe of Judah descended from the man named Judah.  This man was one of the twelve sons of the patriarch Jacob (Genesis 35:23).

Abraham was the father of Isaac (Genesis 21:3).  Isaac was the father of Jacob (Genesis 25:26).  Jacob was the father of Judah (Genesis 35:23).  Judah, the progenitor of the Jews, was a great-grandson of Abraham.  Therefore, Abraham was not a Jew, but an ancestor of the Jews.  Abraham is properly referred to as a Hebrew.