Should I join the military to pay back student loans?

ROTC should be heavily considered. Since you're considering doing service already, check if you're school has an AF or Army ROTC program. You could contract, get a full scholarship, and then do a few years of service afterwards. I warn you though, don't do ROTC if you're gonna be some bullshit Officer that has no interest in the Armed Forces or his Soldiers, there are enough of those. But yeah, look into, it fits your situation perfectly.