Stray cat keeps on coming into my front yard?

There is a misconception that all shelters put down animals because of space issues. That is not so true anymore while yes some do put down animals it is because they are beyond help. Either too sick to fix or because of extreme behavioral problems. If it is a healthy semi friendly cat then you should have no worries. Just call around and see which shelters in your area are able to accept a stray and ask if they have a cat trap you can borrow, some may ask for a fee. but if it gives a cat a better life it is worth it.