I would just go to the state government web site, and rummage around until I find something that sounds like State Parks. There is usually a Search box on the web site. If not, you might look for terms like Recreation, Tourism, Visitors, or whatever sounds promising. The reservation system should be in there.
You could probably do it a bit faster by Googling "Arizona state parks", for example - that should get you there, too.
I am not aware of any nationwide site that covers all the state parks - but I could be wrong.
Bill
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