Archbishop Rajič expressed his “deep gratitude” for the new role entrusted to him by the Pope and for the confidence placed in him, together with his hopes of “being of service” to the Pope and “the universal Church”, Vatican News reported. 

Msgr. Petar Antun Rajič was born into a Croatian family in Toronto on June 12, 1959, to his father, Liberan, and mother, Dominika, née Mustapić.

He was ordained a priest on the Solemnity of Saints Peter and Paul in 1987 at Mostar Cathedral, for service in the Diocese of Trebinje-Mrkan.

After serving as a parish vicar in Toronto for two years (1987–1989), he studied in Rome, where he resided at the Pontifical Croatian College of St. Jerome from 1989 to 1991. In Rome, he attended the Pontifical Ecclesiastical Academy, where he trained for the diplomatic service of the Holy See. In 1993, he obtained a doctorate in Canon Law from the Pontifical Lateran University. That same year, he entered the diplomatic service of the Holy See.

He served as secretary at the Holy See’s diplomatic missions in Iran (1993–1996) and in Lithuania, Estonia and Latvia (1996–1998). He also served as secretary to the Substitute for General Affairs of the Secretariat of State of the Holy See, Archbishop Giovanni Battista Re. From 2003, as a chamberlain or Papal Household prelate, he participated in the organization of the Holy Father’s general and private audiences at the Prefecture of the Papal Household.

On December 2, 2009, Pope Benedict XVI appointed him Titular Archbishop of Sarsenterum and Apostolic Nuncio to the State of Kuwait, the Kingdom of Bahrain and the State of Qatar, while also appointing him Apostolic Delegate to the Arabian Peninsula.

He was ordained a bishop on January 23, 2010, at Mostar Cathedral by then Secretary of State of the Holy See, Cardinal Tarcisio Bertone.

On March 27, 2010, he was appointed Apostolic Nuncio to the Republic of Yemen and the United Arab Emirates. On June 15, 2015, Pope Francis appointed him Apostolic Nuncio to the Republic of Angola and the Democratic Republic of São Tomé and Príncipe. On June 15, 2019, he was appointed Apostolic Nuncio to the Republic of Lithuania, and from August 6 of the same year, also to the Republic of Estonia and the Republic of Latvia.

On March 11, 2024, Pope Francis appointed Msgr. Rajič Apostolic Nuncio to the Italian Republic and the Republic of San Marino.

In addition to English and Croatian, Msgr. Rajič speaks French, Italian and Spanish, according to the Holy See Press Office.