It's definitely a tree frog, depending on where you are located its genus might be Hyla or Pseudacris or something else entirely. You could feed it fruit flies, house flies and small crickets and keep it in terrarium with moist coconut substrate and a water dish to swim about in.
Its a copes tree frog, I had about 5 of them at one time.. they actually change from gray to green at times=))
Oh and I found all mine in wisconsin in the back yard at night ha theyre deff nocturnal.