Hello Jenna:
Sorry to hear that your kitty is missing.
Recently we heard of a person using the cat's litter box to attract the missing cat back to the house.
We either heard it or read it somewhere. If you put the litter box outside, the cat will smell it and should return. According to the article, cats can smell their litter box up to a mile away, so it might work for you. It doesn't matter if it has been scooped out - as long as there is some of the litter left in the box after it has been scooped. Hopefully there hasn't been too much of a time lapse since the cat went missing, for this to work. But it's worth a try.
I am in agreement with Marko because bringing a new animal into the house will require a lot of time and patience.
Best of luck and please keep us informed.