I know it's possible, but couldn't begin to tell you how to get started, to join a Zen Monastery in Japan. You will of course need to be accepted into the Monastery and then use your free time to find an instructor in Japan under whom you can study.
I know it can be done, because it has been done, but as I mentioned before, I haven't the foggiest idea what to tell you as to where to start. If you're looking for something in this country, you aren't gonna find it, and if you do it's probably a cult and you should run away as fast as you can.