Do I need a trappers license to live catch feral cats in my own yard to protect my chickens?
No Fish and Game issued trapping license is needed to catch ferrel cats on your property. Ferel cats would not be classified as wildlife and would not fall under Fish and game jurisdiction.
Ferel cats fall under state, county and city jurisdiction, and therefore you should be aware of animal abuse laws.
I would consult with animal control agents in your local jurisdiction