After his ordination, the archdiocese assigned Parker as associate pastor of St. Peter Parish in Westernport, Maryland. In 2001, he was transferred to St. Michael Parish in Frostburg, Maryland. After four years at St. Michael, the archdiocese appointed him first as administrator of Ascension Parish in Halethorpe, Maryland, then as its pastor.[4] He served simultaneously as the associate director of the Permanent Diaconate Formation Team for the archdiocese from 2006 to 2007.[1]
On December 5, 2016, Pope Francis appointed Parker as an auxiliary bishop of Baltimore and titular bishop of Tasaccora.[5] He was consecrated in the Cathedral of Mary Our Queen in Baltimore on January 19, 2017, by Lori, with Archbishop Edwin O'Brien and Bishop Donald Wuerl serving as co-consecrators.[6][3]