Even if the US only incarcerated rapists and murderers, we would still incarcerate more than Germany. It's not so simple as you're implying.
Still, why call it "land of the free" then? "Land of the most rapists and murderers per capita (or close)" or "Broken society" sounds more apt!
But I'm pretty sure the BS "marijuana laws" and other such incarceration reasons that wouldn't even exist in Germany, are a big part (at least until recently, not sure today) of the disparity.
Germany is around 70 per 100000.
You were saying?
According to the Bureau of Justice Statistics [0], among all state-level prisoners, 14.3% of them are in for murder, and 13.1% are in for rape. That's 27.4% for the combination, or about 350,000 inmates. 106 per 100,000.
If you add in Federal prisoners, the inmate count goes to ~370,000, or about 112/100k
[0] https://www.bjs.gov/content/pub/pdf/p18.pdf (PDF, see table 13, page 21.)