No Pit Bulls are not illegal in Arizona.
On May 19, 2016 Arizona became the 20th state to ban breed specific legislation. Arizona Governor Doug Ducey (R) signed the law.
In the house, 35 Republicans and 1 Democrat (Rep. Reginald Bolding) voted in favor of the law. In the Senate 17 Republicans and 1 Democrat voted in favor of the law.
The bill also include removing the requirements for commercial pet stores from only selling recuse dogs and cats. Bad news for the shelters.
You can read more about the bill here.