I have heard that a person should marry within his or her race. Well if a person is of mixed blood, who does that person marry?
The simple answer to your question is–whoever one wants to!
There is no official Church doctrine against interracial marriages. What some Church leaders have suggested in the past is that, as a practical matter, marriage is hard; and marriages will often run more smoothly when the parties come from similar economic, national, religious, ideological, or ethnic backgrounds. From President Spencer W. Kimball:
We recommend that people marry those who are of the same racial background generally, and of somewhat the same economic and social and educational background (some of those are not an absolute necessity, but preferred), and above all, the same religious background, without question. “Marriage and Divorce,” in 1976 Devotional Speeches of the Year [Provo: Brigham Young University Press, 1977], p. 144
We don’t hear much counsel like this any more. What you choose to do with it, and whether or how you apply it in your own life, is up to you.