As other posters have said, the requirements vary across the nation. I would take a look at where you want to work and look at the specific requirement for the agency. Every agency has a website with recruiting information including the minimum requirements. Generally, the minimum requirements may not make you competitive. It's a good idea to look at a 4 year degree in a biological science major (Wildlife, fisheries, etc). This will not only make you more competitive but it will be better for your career in the long run.
Also look for seasonal or volunteer opportunities. There is no substitute for relevant experience when it comes to competing for a job.
I'm glad you are considering the career of a game warden. It is a very rewarding career and a really fun job!