This claim comes from Peter Schweizer's book Clinton Cash.
The Washington Post notes that the details mentioned above are correct:
The deal gave Russia control of about 20 percent of U.S. uranium
extraction capacity, according to a 2010 CNN article about the deal.
In other words, Russia has rights to the uranium extracted at those
sites, which represents 20 percent of the U.S. uranium production
However, tying it to Clinton is misleading at best. The evidence seems to rest on two facts:
- A Canadian businessman (as noted above) that was instrumental in the
sale was also a Clinton donor.
- The State Department was 1 of 9 agencies surveying the deal.
Details about the deal are not very available, but the State Department did not have the authority to stop the deal. Only the President could, according to the Post.
Clinton has denied that she was involved, and the consensus seems to be that the Secretary would mostly likely not be involved in the details.
There were some concerns raised, but they didn't go to her: Some
Republican lawmakers in 2010 did raise concerns about the deal — but
they sent their letter to then-Treasury Secretary Timothy F. Geithner.
(Treasury chairs the CFIUS.) Final approval was given by the Nuclear
Regulatory Commission, which noted that the mines would remain under
the control of U.S. subsidiaries.
And, as @jeffronicus mentions above, the deal gave the Russian company the right to the profits from the uranium, but not to acquire the uranium itself.
So, in the absence of hard facts, it looks like her agency was one of many involved in approving the deal to sell extraction rights, but that she probably was not involved. In any case, she was not the deciding vote on the review process. You could argue that maybe she could have stopped it, but to answer the question: she was not in the position to "give" anyone anything.