As of my last visit you could not. They currently do not have a camp host on site and this was the reason given by local rangers and the website for no reservations. All sites are currently first come-first served. This could change in the future, so check the website before you go.

I don't believe you can, it's First Come, First served... or whatever it is... Might go to the BLM in CA, not AZ as it's in CA on the Colorado River.. and see this link BLM Calif https://www.blm.gov/visit/crossroads-campground but I don't think BLM takes reservations..