Objection 1. It would seem unfitting that the whole Trinity should adopt. For adoption is said of God in likeness to human custom. But among men those only adopt who can beget: and in God this can be applied only to the Father. Therefore in God the Father alone can adopt.
Objection 2. Further, by adoption men become the brethren of Christ, according to Romans 8:29: "That He might be the first-born among many brethren." Now brethren are the sons of the same father; wherefore our Lord says (John 20:17): "I ascend to My Father and to your Father." Therefore Christ's Father alone has adopted sons.
Objection 3. Further, it is written (Galatians 4:4-6): "God sent His Son... that we might receive the adoption of sons. And because you are sons of God, God hath sent the Spirit of His Son into your hearts, crying: 'Abba' [Father]." Therefore it belongs to Him to adopt, Who has the Son and the Holy Ghost. But this belongs to the Father alone. Therefore it befits the Father alone to adopt.
On the contrary, It belongs to Him to adopt us as sons, Whom we can call Father; whence it is written (Romans 8:15): "You have received the spirit of adoption of sons, whereby we cry: 'Abba' [Father]." But when we say to God, "Our Father," we address the whole Trinity: as is the case with the other names which are said of God in respect of creatures, as stated in I, 33, 3, Objection 1; cf. I, 45, 6. Therefore to adopt is befitting to the whole Trinity.
I answer that, There is this difference between an adopted son of God and the natural Son of God, that the latter is "begotten not made"; whereas the former is made, according to John 1:12: "He gave them power to be made the sons of God." Yet sometimes the adopted son is said to be begotten, by reason of the spiritual regeneration which is by grace, not by nature; wherefore it is written (James 1:18): "Of His own will hath He begotten us by the word of truth." Now although, in God, to beget belongs to the Person of the Father, yet to produce any effect in creatures is common to the whole Trinity, by reason of the oneness of their Nature: since, where there is one nature, there must needs be one power and one operation: whence our Lord says (John 5:19): "What things soever the Father doth, these the Son also doth in like manner." Therefore it belongs to the whole Trinity to adopt men as sons of God.
Reply to Objection 1. All human individuals are not of one individual nature, so that there need be one operation and one effect of them all, as is the case in God. Consequently in this respect no comparison is possible.
Reply to Objection 2. By adoption we are made the brethren of Christ, as having with Him the same Father: Who, nevertheless, is His Father in one way, and ours in another. Whence pointedly our Lord says, separately, "My Father," and "Your Father" (John 20:17). For He is Christ's Father by natural generation; and this is proper to Him: whereas He is our Father by a voluntary operation, which is common to Him and to the Son and Holy Ghost: so that Christ is not the Son of the whole Trinity, as we are.
Reply to Objection 3. As stated above (1, ad 2), adoptive sonship is a certain likeness of the eternal Sonship: just as all that takes place in time is a certain likeness of what has been from eternity. Now man is likened to the splendor of the Eternal Son by reason of the light of grace which is attributed to the Holy Ghost. Therefore adoption, though common to the whole Trinity, is appropriated to the Father as its author; to the Son, as its exemplar; to the Holy Ghost, as imprinting on us the likeness of this exemplar.
Source: Summa Theologica (New Advent)