Well, there's no doubt Biblically-speaking that He was descended from the line of King David. Just reading the Gospel of Luke makes that quite evident, and it's also in accord with many prophetic statements about Him in the Old Testament.
But there's certainly something deeper and more mysterious than just the typical notion of race entails. For example, there are Christophanies in the OT mentioned that occurred before Abraham even existed, and certainly numerous ones before Kind David did. Cf. Genesis & Job for example. Further, as the transcendental and eternal Son of God, what race is that?
When the Godhead held it's eternal council to arrange for the salvation of Man and the ultimate destruction of Satan all in the same plan, what 'race' was Jesus then OP?