Be an Arizona resident. Be at least 18 years of age.Call the Secretary of State's Office, Notary Division at (602) 542-6187. Complete, sign and submit a waiver for a criminal background check. American Association of Notaries offers free step-by-step instructions on how to complete your Arizona notary application and apply to become an Arizona notary. Complete a notary application. • Take and pass the test. Application Procedures. Step 1: Complete the Mandatory Notary Training and Online Exam. Complete the declaration application.