
You'll need to check specific requirements, the (as of writing) somewhat right wing governement may be making access to work visas more difficult for foreigners, and since the profession essentially doesn't exist in Austria, it is even more complicated. If already an EU passport holder, then read on...
In Austria Chiropractic is neither a legalised nor a regulated profession. Only MDs with manual treatment certification can officially offer "chirotherapeutic" conservative therapy. Even Osteopaths and Physiotherapists officially would need a referral from an MD for any manual intervention, especially for any kind of manipulative techniques. Practicing straight Vitalistic Chiropractic on first contact is definitely in the 'outlaw darkgrey zone'. No Insurance covers Chiropractic.