It is hard to put an exact number on it, as not every master or overseer was going to be keeping track, but rape (and I use rape here because no matter how willing to go along with the act a given slave might have been, the power dynamics of the relationship should unnerve anyone, so lets not get into a semantic debate) of black slave women by whites was very common, and we can trace this fact through genetic testing.

I did a brief explanation of this previously, which I'll copy paste for you here:

Anyways, the rise of cheap, easy DNA testing has been a real boon for people looking into their roots, and also has given us some very interesting peeks into history. A little while back, TheRoot.com published a piece summarizing the findings of mass-market DNA testing companies from when they analyzed African-American DNA.

What did they find? Depending on the company, the average percentage of DNA in African-Americans that was of European ancestry was between 19 percent and 29 percent. For the patrilineal line specifically (father's father's father's etc), 35 percent of African-Americans would eventually hit a white ancestor. And of course that doesn't account for maternal great-x-grandfathers. If we assume that the white DNA is almost exclusively coming from a male ancestor (not to say it couldn't happen where a white woman slept with a black man, but I think it reasonable to assume it happened less frequently), than we can double those numbers, and say that the average African-American's forefathers are very white. Between 38 and 58 percent in fact. I would think the implications of that are clear, but just to drive home the point, a LOT of that comes from masters or foremen having sex with African-American slaves, possibly in violent circumstances, but almost certainly as part of a coercive relationship where they couldn't exactly say "sorry, I have a headache tonight".

The TL;DR is that the average African-American is actually 1/4 "white".