Objection 1. It would seem that to swear is not to call God to witness. Whoever invokes the authority of Holy Writ calls God to witness, since it is His word that Holy Writ contains. Therefore, if to swear is to call God to witness, whoever invoked the authority of Holy Writ would swear.
But this is false Therefore the antecedent is false also.
Objection 2. Further, one does not pay anything to a person by calling him to witness. But he who swears by God pays something to Him for it is written (Matthew 5:33): "Thou shall pay [Douay: 'perform'] thy oaths to the Lord"; and Augustine says [Serm. clxxx] that to swear [jurare] is "to pay the right [jus reddere] of truth to God." Therefore to swear is not to call God to witness.
Objection 3. Further, the duties of a judge differ from the duties of a witness, as shown above (Q67,70). Now sometimes a man, by swearing, implores the Divine judgment, according to Psalm 7:5, "If I have rendered to them that repaid me evils, let me deservedly fall empty before my enemies." Therefore to swear is not to call God to witness.
On the contrary, Augustine says in a sermon on perjury (Serm. clxxx): "When a man says: 'By God,' what else does he mean but that God is his witness?"
I answer that, As the Apostle says (Hebrews 6:16), oaths are taken for the purpose of confirmation. Now speculative propositions receive confirmation from reason, which proceeds from principles known naturally and infallibly true. But particular contingent facts regarding man cannot be confirmed by a necessary reason, wherefore propositions regarding such things are wont to be confirmed by witnesses. Now a human witness does not suffice to confirm such matters for two reasons. First, on account of man's lack of truth, for many give way to lying, according to Psalm 16:10, "Their mouth hath spoken lies [Vulgate: 'proudly']." Secondly, on account of this lack of knowledge, since he can know neither the future, nor secret thoughts, nor distant things: and yet men speak about such things, and our everyday life requires that we should have some certitude about them. Hence the need to have recourse to a Divine witness, for neither can God lie, nor is anything hidden from Him. Now to call God to witness is named "jurare" [to swear] because it is established as though it were a principle of law [jure] that what a man asserts under the invocation of God as His witness should be accepted as true. Now sometimes God is called to witness when we assert present or past events, and this is termed a "declaratory oath"; while sometimes God is called to witness in confirmation of something future, and this is termed a "promissory oath."
But oaths are not employed in order to substantiate necessary matters, and such as come under the investigation of reason; for it would seem absurd in a scientific discussion to wish to prove one's point by an oath.
Reply to Objection 1. It is one thing to employ a Divine witness already given, as when one adduces the authority of Holy Scripture; and another to implore God to bear witness, as in an oath.
Reply to Objection 2. A man is said to pay his oaths to God because he performs what he swears to do, or because, from the very fact that he calls upon God to witness, he recognizes Him as possessing universal knowledge and unerring truth.
Reply to Objection 3. A person is called to give witness, in order that he may make known the truth about what is alleged. Now there are two ways in which God makes known whether the alleged facts are true or not. On one way He reveals the truth simply, either by inward inspiration, or by unveiling the facts, namely, by making public what was hitherto secret: in another way by punishing the lying witness, and then He is at once judge and witness, since by punishing the liar He makes known his lie. Hence oaths are of two kinds: one is a simple contestation of God, as when a man says "God is my witness," or, "I speak before God," or, "By God," which has the same meaning, as Augustine states [See argument On the contrary]; the other is by cursing, and consists in a man binding himself or something of his to punishment if what is alleged be not true.
Source: Summa Theologica (New Advent)