The answer, in essence, is “no.”
In principle, there is no obstacle to the marriage of any baptized Catholic man to any baptized Catholic woman, regardless of race.
This is a principle at least as old as St. Paul:
For as many of you as were baptized into Christ have put on Christ. There is neither Jew nor Greek, there is neither slave nor free, there is no male and female, for you are all one in Christ Jesus (Galatians 3:27-28).
Evidently, St. Paul is addressing baptized Jews and Greeks here, and Baptism removes all of the barriers to communion that man commonly places: race, social status, and sex.
(Since the O.P. mentions the homosexual marriage issue, please note that St. Paul is by no means downplaying the complementarity of the sexes in this passage; he is simply saying that neither men nor women are prevented from enjoying full communion in Christ. All too often—especially in the ancient world—women have endured a status as second-class citizens; St. Paul is saying that there are no second-class citizens in the Church.)
I was unable to find any official Church document that addresses the issue of interracial marriage directly, but Canon Law places no restriction whatsoever on race (neither the current code nor the older code issued in 1917).
There have doubtless been individual parishes that have refused marriages to interracial couples, but in general the Church has never refused such marriages.
Regarding interracial marriage as an argument for homosexual marriage: it is true that many states in the Jim Crow era prohibited interracial marriage (what the Catholic Church would call civil marriage, which is simply the legal contract established by spouses, not the Sacrament of Matrimony). Doubtless many Christian denominations followed suit (however, not the Catholic Church as a body).
However, it is a logical fallacy—a classic non sequitur—to deduce from this fact that therefore opposition to same-sex marriage is based on prejudices similar to those of the Jim Crow era.
In reality, “race” is an artificial concept that has no true basis in human nature. (It is true that human beings from different ethnic origins often have slightly different external characteristics, but these differences are quite superficial.) On the other hand, the complementarity of the sexes is indeed based on reality. Hence, there is no comparison between interracial marriage and homosexual marriage.