Angelo Rizzo studied at the seminary of Caltanissetta Catholic theology and philosophy. Rizzo was consecrated on 31 October 1948 to the priest. He was chancellor of and prefect of studies at the seminary of Caltanissetta. 1965 Angelo Rizzo was appointed archpriest of Montedoro and the Director of the Office for Catechesis of the Diocese of Caltanissetta. In addition, he was a canon at the Santa Maria La Nova Cathedral.
On 2 February 1974, he was appointed bishop of Ragusa. He received his episcopal consecration on March 18 of the same year the Archbishop of Palermo, Salvatore Cardinal Pappalardo; Co-consecrators were the Bishop of Caltanissetta, Alfredo Maria Garsia, and the retired Bishop of Caltanissetta, Francesco Monaco. In the Italian Episcopal Conference Rizzo was a member of the Commission for the Laity. His age-related resignation was accepted by Pope John Paul II on 16 February 2002.