First you have to catch them. And then you have to give them 'the shot' - by which I assume you mean killing them in a 'humane' way.
Guess what - someone has to pay. If a farm owner in rural wisconsin catches a cat going after his chickens, he has the right to take care of the problem with a .22 lr - instead of having to call animal control and getting a bill for it.
I had a chicken escape its farm to get into my garage. It would have been fair game for my cat.