In Hawaii there are feral game chickens without predators that are a huge nuisance: noise, garden destruction, disease. I sympathize, believe me. I have used a live trap to great success, the kind that you use to catch raccoons or feral cats and such, with a trip plate on the floor of the cage that springs the door. There are many other models that would work too. I have also used "deadly force," but I have actually found the live trap to be the most effective weapon overall anyway. They are effective, easy, and humane. Bait it with a tiny handful of chicken feed or grain or pieces of fruit, and check it frequently to make sure you aren't catching other things (cats, doves) and rebait if doves or sparrows are eating the bait. When I catch them I dislocate their necks to "euthanize" them, but if this bothers you you could always relocate the rooster--and make him someone elses problem.
Anyway, good luck.