Yes. Go to the "official website" link on the Campendium page and call the number. There are only 12 sites, so you should make a reservation. If you show up without a reservation, look at the chart on the office door at the park entrance, choose a site that's vacant for the period you want, and write yourself in on the chart.
It has been a couple years ago but I think if you can find Bingham County and check
https://www.co.bingham.id.us/parks_recreation/north_bingham_park.html