In Christian art, saints are often depicted with various symbols that represent different aspects of their life. When it comes to the Gospel writers, they too have very specific symbols that summarize key themes in their Gospels. St. Luke in particular is represented by an ox or calf, a sacrificial animal in ancient Judaism.
One reason for this representation is that St. Luke's Gospel emphasizes the sacrifice of Jesus Christ on the cross.
The Catholic Encyclopedia also explains that "St. Luke its always represented by the calf or ox, the sacrificial animal, because his Gospel begins with the account of Zachary, the priest, the father of John the Baptist."
Zachariah is in the Temple offering a sacrifice of incense when he encounters an angel, who tells him about the birth of his son, John the Baptist (cf. Luke 1).
Depicting St. Luke with an ox or calf gave Christians a basic summary of his Gospel, reminding them how he focused on the theme of sacrifice.
