Can I get back into the Army after being out since 2012 and having a DD-214 that says JCR 3?

If you're meaning an RE-3 code, you'll need a waiver. Talk to a Recruiter for the details and process

I just looked at your profile. You're going to have some significant hurdles to come back in. Dependents, RCP, and RE Code are what I see as issues right off the bat. I would have to agree with SFC Livingston suggesting you talk to a recruiter. The main thing to remember is to tell them everything surrounding your situation. Leaving things out because you don't think they're a big deal will come back to bite you 9 times out of 10 and you could end up wasting a lot of time. Best of luck to you.