While the Jewish people began with the descendents of Abraham, Isaac and Jacob, many people have converted to become Jews over the millennia--beginning with the "mixed multitude" that came with us out of Egypt. Today there are African Jews, Japanese Jews, even Eskimo Jews. It seems difficult to call such a mixture a "race".
(Incidently, there is really no such thing as a "race." The term "race" implies to most people that there are different categories of human beings based on their genetic makeup. The fact is that there is no basis in genetics for these distinctions. For example, an African from one family may have more in common genetically with a Swede than with another African.)
What could be said is that we are a "family". A family can adopt others as their own. But there are conditions to adoption. You need to keep the family rules. In our case, those rules have to do with the mission we were given at Mount Sinai over 3300 years ago.