Technically you can do it but it will be a bit difficult. Your going to have to fluent and I believe you have to meet the following requirements:
1. Continuous residence in Japan for five years or more
2. At least 20 years old and otherwise legally competent
3. History of good behavior generally, and no past history of seditious behavior
4. Sufficient capital or skills, either personally or within family, to support oneself
5. Stateless or willing to renounce foreign citizenship
I say technically because I pretty sure it's never been done before. Double check that information, but I'm pretty sure it's accurate. Definitely do JET as it will get your foot in the door. Once in Japan, research as much as you can about it. Try and get into the See if you can find someone who has done this before. If you can't you'll have the privilege of being the first. A true Pioneer!
Below is a brief overview of the Japanese police force a la Wikipedia
Law enforcement in Japan - Wikipedia, the free encyclopedia
check this out to:
Japanese Police Officers