They use wastewater

Edit cause fatfingered send- Nuke plants use massive amounts of water. Hence why they are typically built near rivers. However, obviously, desert areas don't have this luxury. So they use treated wastewater as a water source. That said, there technically is water almost anywhere. The issue with most areas like these, is that water has high mineral and salt content. Then there's also the issue with local landowners, who the power companies would have to cooperate with in order to drill for it. Arizona does have waterlogged areas where water can be found, but as with all drilling, those permits need to be issued by the State and the locals