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That's about proportionate with the total population.
Let's see 'per capita' for everyone else.
If you visit the link that I provided, it breaks down the percentages for each race: 57% of rapists are white, 27% black, 8% unknown, 6% other, and 1% mixed race.
I did a little investigation, and was able to find the source material for the statistics RAINN cited
here. I feel like it's worth noting that these statistics only concern rapes that are
reported to the police - it doesn't include all rapes. Also, it says the racial statistics are based on
perceived race of the perpetrator, so I would lay odds that the "black" statistic more accurately would be represented by calling it "dark-skinned" and probably contains a bunch of Middle Eastern and South Asian dudes as well. Note this is not me saying that black men don't rape or whatever, just acknowledging that racial identification in the US is pretty universally shit and men of all races commit rape. Keeping that in mind, if you add the numbers for black, unknown, mixed and other rapists together, you get roughly the same % as if you put together the percent of Americans who are black, non-white Latinos, Asian, other and mixed race.
It feels like common sense is the winner here: All races of men rape pretty much at the same rates, so the rate of each racial category of men committing rape is likely pretty close to the percentage of the population their racial category comprises.