I personally know more than one person who has worked in the cage, they are paid above minimum wage. It's not a great salary or anything, but it's not minimum wage or below. The $30,000/year that a sibling comment says sounds right. The BLS considers them "financial clerks" and doesn't break out casino employees separately[1].
The average Cage Cashier - Casino salary in the United States is $30,943 as of September 01, 2018, but the range typically falls between $25,713 and $39,285.
Source: Salary for Cage Cashier - Casino | Salary.com
I found no evidence they are paid less than minimum wage, but I did find some claims casino-goers in the US are expected to tip cashiers, so perhaps the assumption is they are paid a tipped minimum wage instead of a regular one? That is not how jobs seem to be advertised though.
I’m no high roller, nor even much of a casino customer anymore, but having cashed in many tens of thousands of dollars of chips it would have never occurred to me to tip a cage cashier. They seem so disinterested in the fact that I’m standing there, it is not like they’re trying for tips. Nor have I even heard it mentioned. Now, I’m not a complete rube as I tip table and wait staff (heavily, if I’ve won big). But the person doing what I expect a casino to do: exchange their fake money for fiat? Never.
They actually do. Google it. It's below minimum.