 McShea was ordained a priest by Cardinal Francesco Marchetti Selvaggiani on December 6, 1931.His first assignment, following his return to Pennsylvania, was as a professor at St. Charles Borromeo Seminary, where taught Latin, Italian, and history (1932–35).From 1935 to 1938, he served as a "minutante" of the Congregation for the Oriental Churches in the Roman Curia.