There is nothing in the Bible saying it is wrong to date or marry a person of a different race.
There are a few incidental mentions of race in the Bible (e.g., that Ethiopian's skin was different, Jeremiah ), but there is nothing saying one race is superior to another.
If you're looking for answers here, then you're already well on your way to learning how God wants you to handle relationships with the opposite sex.
Many of the dating and personal relationship safeguards of years gone by seem to have been cast aside.
In most aspects of modern life, God doesn’t provide cookie-cutter answers or formulas.
But be encouraged, though He may not always provide us with the direct plan, He always gives us everything we need to get where He wants us to go.
I suspect that this would be an inferential conclusion, and thus would have to be considered a matter of personal conviction, rather than as a clear biblical prohibition.
One could certainly ask, “If a Christian cannot marry an unbeliever, why would they ever date one? I think one can have a friendship relationship with an unbeliever of the opposite sex, without entering into a dating relationship.