How can I get an RE-3 waiver, and where do I apply for it?

PVT (Join to see) Sit down while I tell you my tale (lol).
I, too, had an RE3. I had served Active Air Force as Security Forces when I was given a medical discharge after 1.5 yrs.
I went through 3 different recruiters before I ran into the recruiter that actually managed to get me processed back in; the others up and disappeared like a fart in the wind at the first sign of difficulty.
First, I had to get a waiver just to go to MEPS. Then, after about 3 trips to MEPS, they cleared me to get a Surgeon General's waiver. Once the SG waiver came through, THEN I was allowed to officially come back.
The recruiter knew her stuff, and had all the dominoes lined up before I hit each step, so they would all be ready to fall in succession. This whole journey took me 18.5 years.

The moral: EVERY SINGLE PIECE of paperwork you have for the discharge, reasoning for the code, and anything that indicates the reasoning for the code no longer exists, and a kickass recruiter. Beyond that, it is in the hands of the powers that be.

PVT (Join to see)

In the case of the Army, you work through a recruiter. http://arba.army.pentagon.mil/adrb-faq.html

The Army Discharge Review Board will not upgrade a RE3/4 unless it was an administrative error. You have to work with a recruiter who helps you initiate a waiver request. I would assume the USNUSMC works the same way.

All services Discharge review boards via NPRC:

https://www.archives.gov/personnel-records-center/vso/boards-for-correction-of-military-records

AR 601-210 Chapter 3 will give you an idea of what you are up against.

Recommend editing your original post and tag it with the following topics: RE Code, Marine recruiting, Army Recruiting, Discharges, and if it is in there classification of Discharge. There are a couple hundred discussions on this type of topic. You need to tap into those.

There are hundreds of post on this site that explain this process, search them out and you will see the answer is (best answer anyway) You need to talk with your recruiter.... They process everything to do with waivers, take all your paperwork in to them, everything, and ask them to process a waiver for enlistment.

Also - if you did not pass BCT and AIT it will not be considered and re-enlistment; rather a Glossy NPS enlistment, so you will have to go through everything again MEPS/BCT/AIT... best of luck to you.