[1] While in Rome, Morkovsky was ordained to the priesthood for the Archdiocese of San Antonio by Cardinal Francesco Marchetti Selvaggiani on December 5, 1933.
[1] He briefly served as pastor of St. Francis de Paula Parish and superintendent of Catholic schools in San Antonio.
[1] In 1941, Morkovsky was sent to Washington, D.C. to study at the Catholic University of America, obtaining a Master of Arts degree in education.
[2] During that time, he also held the following posts: Morkovsky also organized the Federation of Catholic Parents' and Teachers' Clubs in San Antonio.
[3] He received his episcopal consecration on February 22, 1956, from Archbishop Amleto Cicognani, with Bishops Mariano Garriga and Sidney Metzger serving as co-consecrators.
In 1964 he founded the diocesan newspaper The Texas Catholic Herald and hosted the visit of Cardinal Josef Beran.
[2] Morkovsky established the first diocesan mission in Guatemala City in 1966, and the Hospital Chaplains Corps at Houston Medical Center in 1968.