Objection 1. It would seem that it is not lawful to swear. Nothing forbidden in the Divine Law is lawful. Now swearing is forbidden (Matthew 5:34), "But I say to you not to swear at all"; and (James 5:12), "Above all things, my brethren, swear not." Therefore swearing is unlawful.
Objection 2. Further, whatever comes from an evil seems to be unlawful, because according to Matthew 7:18, "neither can an evil tree bring forth good fruit." Now swearing comes from an evil, for it is written (Matthew 5:37): "But let your speech be: Yea, yea: No, no. And that which is over and above these is of evil." Therefore swearing is apparently unlawful.
Objection 3. Further, to seek a sign of Divine Providence is to tempt God, and this is altogether unlawful, according to Deuteronomy 6:16, "Thou shalt not tempt the Lord thy God." Now he that swears seems to seek a sign of Divine Providence, since he asks God to bear witness, and this must be by some evident effect. Therefore it seems that swearing is altogether unlawful.
On the contrary, It is written (Deuteronomy 6:13): "Thou shalt fear the Lord thy God... and shalt swear by His name."
I answer that, Nothing prevents a thing being good in itself, and yet becoming a source of evil to one who makes use thereof unbecomingly: thus to receive the Eucharist is good, and yet he that receives it "unworthily, eateth and drinketh judgment to himself" (1 Corinthians 11:29). Accordingly in answer to the question in point it must be stated that an oath is in itself lawful and commendable. This is proved from its origin and from its end. From its origin, because swearing owes its introduction to the faith whereby man believes that God possesses unerring truth and universal knowledge and foresight of all things: and from its end, since oaths are employed in order to justify men, and to put an end to controversy (Hebrews 6:16).
Yet an oath becomes a source of evil to him that makes evil use of it, that is who employs it without necessity and due caution. For if a man calls God as witness, for some trifling reason, it would seemingly prove him to have but little reverence for God, since he would not treat even a good man in this manner. Moreover, he is in danger of committing perjury, because man easily offends in words, according to James 3:2, "If any man offend not in word, the same is a perfect man." Wherefore it is written (Sirach 23:9): "Let not thy mouth be accustomed to swearing, for in it there are many falls."
Reply to Objection 1. Jerome, commenting on Matthew 5:34, says: "Observe that our Saviour forbade us to swear, not by God, but by heaven and earth. For it is known that the Jews have this most evil custom of swearing by the elements." Yet this answer does not suffice, because James adds, "nor by any other oath." Wherefore we must reply that, as Augustine states (De Mendacio xv), "when the Apostle employs an oath in his epistles, he shows how we are to understand the saying, 'I say to you, not to swear at all'; lest, to wit, swearing lead us to swear easily and from swearing easily, we contract the habit, and, from swearing habitually, we fall into perjury. Hence we find that he swore only when writing, because thought brings caution and avoids hasty words."
Reply to Objection 2. According to Augustine (De Serm. Dom. in Monte i. 17): "If you have to swear, note that the necessity arises from the infirmity of those whom you convince, which infirmity is indeed an evil. Accordingly He did not say: 'That which is over and above is evil,' but 'is of evil.' For you do no evil; since you make good use of swearing, by persuading another to a useful purpose: yet it 'comes of the evil' of the person by whose infirmity you are forced to swear."
Reply to Objection 3. He who swears tempts not God, because it is not without usefulness and necessity that he implores the Divine assistance. Moreover, he does not expose himself to danger, if God be unwilling to bear witness there and then: for He certainly will bear witness at some future time, when He "will bring to light the hidden things of darkness, and will make manifest the counsels of hearts" (1 Corinthians 4:5). And this witness will be lacking to none who swears, neither for nor against him.
Source: Summa Theologica (New Advent)