would it be possible to get work as a cop if your a foreigner? I was an MP(military police)in the U.S. so would I be able to apply for a work visa or something?

It would be quite an interesting career path i must say, also somthing like the Fire service (was going to apply in my own country). But being realistic i would imagine they would really only hire Japanese people for this type of work. It would require an extremely high level of Japanese and also quite deep knowledge of the structure of the their law system, sociology, psychology etc and also possibly long enough training periods like in most countries. Also note some countries require citizenship before you can apply for such work.

Your spoken and written Japanese would need to be perfect.. the cultural aspects would be... impossible.
I have NEVER seen a non-Japanese cop and don't expect I ever will.

You would be naturalised, which takes a minimum of 10 years. Unless you are married to a national.

You would also need native level Japanese, which is quite difficult.

I have seen a significant number of foreign police here. So it is possible. Though I'm sure it's difficult.