Objection 1. It would seem that it is not lawful to swear by creatures. It is written (Matthew 5:34-36): "I say to you not to swear at all, neither by heaven... nor by the earth... nor by Jerusalem... nor by thy head": and Jerome, expounding these words, says: "Observe that the Saviour does not forbid swearing by God, but by heaven and earth," etc.
Objection 2. Further, punishment is not due save for a fault. Now a punishment is appointed for one who swears by creatures: for it is written (22, qu. i, can. Clericum): "If a cleric swears by creatures he must be very severely rebuked: and if he shall persist in this vicious habit we wish that he be excommunicated." Therefore it is unlawful to swear by creatures.
Objection 3. Further, an oath is an act of religion, as stated above (Article 4).
But religious worship is not due to any creature, according to Romans 1:23-25. Therefore it is not lawful to swear by a creature.
On the contrary, Joseph swore "by the health of Pharaoh" (Genesis 42:16). Moreover it is customary to swear by the Gospel, by relics, and by the saints.
I answer that, As stated above (1, ad 3), there are two kinds of oath. One is uttered a simple contestation or calling God as witness: and this kind of oath, like faith, is based on God's truth. Now faith is essentially and chiefly about God Who is the very truth, and secondarily about creatures in which God's truth is reflected, as stated above (Question 1, Article 1). On like manner an oath is chiefly referred to God Whose testimony is invoked; and secondarily an appeal by oath is made to certain creatures considered, not in themselves, but as reflecting the Divine truth. Thus we swear by the Gospel, i.e. by God Whose truth is made known in the Gospel; and by the saints who believed this truth and kept it.
The other way of swearing is by cursing and in this kind of oath a creature is adduced that the judgment of God may be wrought therein. Thus a man is wont to swear by his head, or by his son, or by some other thing that he loves, even as the Apostle swore (2 Corinthians 1:23), saying: "I call God to witness upon my soul."
As to Joseph's oath by the health of Pharaoh this may be understood in both ways: either by way of a curse, as though he pledged Pharao's health to God; or by way of contestation, as though he appealed to the truth of God's justice which the princes of the earth are appointed to execute.
Reply to Objection 1. Our Lord forbade us to swear by creatures so as to give them the reverence due to God. Hence Jerome adds that "the Jews, through swearing by the angels and the like, worshipped creatures with a Divine honor."
In the same sense a cleric is punished, according to the canons (22, qu. i, can. Clericum, Objection 2), for swearing by a creature, for this savors of the blasphemy of unbelief. Hence in the next chapter, it is said: "If any one swears by God's hair or head, or otherwise utter blasphemy against God, and he be in ecclesiastical orders, let him be degraded."
This suffices for the Reply to the Second Objection.
Reply to Objection 3. Religious worship is shown to one whose testimony is invoked by oath: hence the prohibition (Exodus 23:13): "By the name of strange gods you shall not swear." But religious worship is not given to creatures employed in an oath in the ways mentioned above.
Source: Summa Theologica (New Advent)