Objection 1. It would seem that an oath is not an act of religion, or latria. Acts of religion are about holy and divine things. But oaths are employed in connection with human disputes, as the Apostle declares (Hebrews 6:16). Therefore swearing is not an act of religion or latria.
Objection 2. Further, it belongs to religion to give worship to God, as Tully says (De Invent. Rhet. ii, 53). But he who swears offers nothing to God, but calls God to be his witness. Therefore swearing is not an act of religion or latria.
Objection 3. Further, the end of religion or latria is to show reverence to God. But the end of an oath is not this, but rather the confirmation of some assertion. Therefore swearing is not an act of religion.
On the contrary, It is written (Deuteronomy 6:13): "Thou shalt fear the Lord thy God, and shalt serve Him only, and thou shalt swear by His name." Now he speaks there of the servitude of religion. Therefore swearing is an act of religion.
I answer that, As appears from what has been said above (Article 1), he that swears calls God to witness in confirmation of what he says. Now nothing is confirmed save by what is more certain and more powerful. Therefore in the very fact that a man swears by God, he acknowledges God to be more powerful, by reason of His unfailing truth and His universal knowledge; and thus in a way he shows reverence to God. For this reason the Apostle says (Hebrews 6:16) that "men swear by one greater than themselves," and Jerome commenting on Matthew 5:34, says that "he who swears either reveres or loves the person by whom he swears." The Philosopher, too, states (Metaph. i, 3) that "to swear is to give very great honor." Now to show reverence to God belongs to religion or latria. wherefore it is evident that an oath is an act of religion or latria.
Reply to Objection 1. Two things may be observed in an oath. The witness adduced, and this is Divine: and the thing witnessed to, or that which makes it necessary to call the witness, and this is human. Accordingly an oath belongs to religion by reason of the former, and not of the latter.
Reply to Objection 2. In the very fact that a man takes God as witness by way of an oath, he acknowledges Him to be greater: and this pertains to the reverence and honor of God, so that he offers something to God, namely, reverence and honor.
Reply to Objection 3. Whatsoever we do, we should do it in honor of God: wherefore there is no hindrance, if by intending to assure a man, we show reverence to God. For we ought so to perform our actions in God's honor that they may conduce to our neighbor's good, since God also works for His own glory and for our good.
Source: Summa Theologica (New Advent)