I did a little research ... using figures from Wikipedia though, so I may have lost a little accuracy, but probably not enough to kill the point given that I chose to use lower of the estimates for Russia...
1937 census in Russia, which pissed off Stalin because it was lower than he wanted so was likely accurate ... 162 million people, 2.6 million in the gulag system and alive. That is 1.6% of the population in the gulag alone, so we'd need those in the prison system too (they were separate).
2011 census in US ... 310 million people, 2.2 million in prison (federal, state or county). That is 0.7% of the population, half of Russia's gulag vs pop calculation.
So I'll assume you truly meant "sent to" rather than "in", and that rate is greater in the US now then in Russia. So either the US has a lot of recidivism, shorter stays, or both. But I imagine that the people who died in the gulag, not included here, would be a higher rate than the United States prison system based on books read on the subject. Not to mention there are plenty of other gulag/prison estimates for Russia that are significantly higher in earlier and later years. So overall, I'd say that the gulag/prison situation, as a percentage of population, seems considerably worse in Russia than today's US. Regardless of the annual rate at which people were sent there.