One really needs to define the term “race” before discussing marriage between races.  “Race” is an ill-defined term.  A hundred years or so ago the term “race” was used to describe different nations, such as the German race or the French race.  Today “race” is used to describe a population of people with similar physical traits, such as Caucasian or Black.  In fact, some Bible students argue that there are the only three races, Caucasian, Asian, and Black, which stem from the three sons of Noah. 

Regardless of what people look like, all of humanity comes from one blood.

Act 17:26  And He has made from one blood every nation of men to dwell on all the face of the earth, and has determined their preappointed times and the boundaries of their dwellings,

All of us can trace our lineage back to the first woman, Eve.

Gen 3:20  And Adam called his wife’s name Eve, because she was the mother of all living.

Humanity is one enormous family.  We are all related to each other.  There is really only one “race”, the human race.

Perhaps a better question to ask is, “Does God place any restrictions on marriage based on physical appearance?”  The answer is, No.  There are no Scriptures where God places restrictions on marriage based on physical appearance.

However, God did place a restriction on ancient Irael.  He told them not to marry into the pagan nations.

Deu 7:3  Nor shall you make marriages with them [Hittites, Amorites, Canaanites, etc.]. You shall not give your daughter to their son, nor take their daughter for your son.

But the reason was not due to their physical appearance, but because they would turn Israel away from following God.

Deu 7:4  For they will turn your sons away from following Me, to serve other gods; so the anger of the LORD will be aroused against you and destroy you suddenly.

A similar admonition is found in the New Testament, which could be applied to marriage.

2Co 6:14  Do not be unequally yoked together with unbelievers. For what fellowship has righteousness with lawlessness? And what communion has light with darkness?

These restrictions are to do with character, not physical appearance.

Conclusion

Interracial marriage is not a sin.