Pope Francis named him Substitute for the Secretariat of State on 15 August 2018, effective 15 October, making him the highest ranking Venezuelan in the Roman Curia.

He fulfilled assignments in Kenya, Yugoslavia (1997–99), South Africa, Honduras (2002–05), and Mexico (2006–11), with a brief stint in the office of the Holy See's representative to the United Nations in Geneva.

[1][7] On 8 January 2011, Pope Benedict XVI appointed Parra titular archbishop of Thélepte and gave him the title "Apostolic Nuncio".

[13][14] Testifying before the High Court of England and Wales on 4 July 2024, Peña Parra stated that he willingly signed off on fraudulent invoices he knew were "completely fictitious" involving Vatican investment properties in London.

[15] In September 2024 Archbishop Peña Parra issued an order trying to reinstate a former priest, Ariel Alberto Príncipi, convicted of child sexual abuse by two interdiocesan tribunals in Argentina.