Can you take your road test in Arizona without taking drivers training?

Yes, with the approval of a parent or guardian. "An applicant must have satisfactorily completed a driver education program that is approved by MVD or the parent or guardian must certify in writing that the applicant has completed at least 30 hours of supervised driving practice, including at least 10 hours at night." http://www.azdot.gov/mvd/faqs/scripts/faqs.asp?section=dl#8