In 2011, the Arizona Legislature DID NOT PASS SB 1538, a bill that makes it a traffic violation with possible fines and penalties if a person is texting while driving. Learn more about SB 1538, by going to the Arizona legislature's website.
The LawForKids.org "Debate it!" legislature would have passed this bill.
However beware that simply because something is not prohibited under Arizona state law, it may still be illegal under the local law of a particular city or county. For example, the City of Phoenix has a law making it illegal to send text messages while driving: Phoenix City Code 36-76.01. Tucson also has a law prohibiting texting while driving, Code 20-160. To check your city's laws, visit the city website; most cities either post their codes and ordinances online, or link to a site that houses their laws.