I wouldn't really suggest trying to keep a snake you found in your yard...I don't have any experience with it myself but I would be worried about internal/external parasites to start with. You would need to find out proper care requirements for a green rat snake, set up a fitting enclosure and get it to the vet for a fecal test and treat it for any parasite load it has. In addition to that, you may have problems feeding it, as it's wild and the mouse pinkies you offer may not be its normal food source. That, and the stress of suddenly being captive might cause it to be reluctant to feed. Some states also have laws against capturing/keeping local species so you should check into that as well.

Taking all those things into consideration, I would be reluctant to try and keep it...