Objection 1. It would seem that the angels cannot know God by their natural principles. For Dionysius says (Div. Nom. i) that God "by His incomprehensible might is placed above all heavenly minds." Afterwards he adds that, "since He is above all substances, He is remote from all knowledge."
Objection 2. Further, God is infinitely above the intellect of an angel. But what is infinitely beyond cannot be reached. Therefore it appears that an angel cannot know God by his natural principles.
Objection 3. Further, it is written (1 Corinthians 13:12): "We see now through a glass in a dark manner; but then face to face." From this it appears that there is a twofold knowledge of God; the one, whereby He is seen in His essence, according to which He is said to be seen face to face; the other whereby He is seen in the mirror of creatures. As was already shown (12, 4), an angel cannot have the former knowledge by his natural principles. Nor does vision through a mirror belong to the angels, since they do not derive their knowledge of God from sensible things, as Dionysius observes (Div. Nom. vii). Therefore the angels cannot know God by their natural powers.
On the contrary, The angels are mightier in knowledge than men. Yet men can know God through their natural principles; according to Romans 1:19: "what is known of God is manifest in them." Therefore much more so can the angels.
I answer that, The angels can have some knowledge of God by their own principles. In evidence whereof it must be borne in mind that a thing is known in three ways: first, by the presence of its essence in the knower, as light can be seen in the eye; and so we have said that an angel knows himself--secondly, by the presence of its similitude in the power which knows it, as a stone is seen by the eye from its image being in the eye--thirdly, when the image of the object known is not drawn directly from the object itself, but from something else in which it is made to appear, as when we behold a man in a mirror.
To the first-named class that knowledge of God is likened by which He is seen through His essence; and knowledge such as this cannot accrue to any creature from its natural principles, as was said above (Question 12, Article 4). The third class comprises the knowledge whereby we know God while we are on earth, by His likeness reflected in creatures, according to Romans 1:20: "The invisible things of God are clearly seen, being understood by the things that are made." Hence, too, we are said to see God in a mirror. But the knowledge, whereby according to his natural principles the angel knows God, stands midway between these two; and is likened to that knowledge whereby a thing is seen through the species abstracted from it. For since God's image is impressed on the very nature of the angel in his essence, the angel knows God in as much as he is the image of God. Yet he does not behold God's essence; because no created likeness is sufficient to represent the Divine essence. Such knowledge then approaches rather to the specular kind; because the angelic nature is itself a kind of mirror representing the Divine image.
Reply to Objection 1. Dionysius is speaking of the knowledge of comprehension, as his words expressly state. In this way God is not known by any created intellect.
Reply to Objection 2. Since an angel's intellect and essence are infinitely remote from God, it follows that he cannot comprehend Him; nor can he see God's essence through his own nature. Yet it does not follow on that account that he can have no knowledge of Him at all: because, as God is infinitely remote from the angel, so the knowledge which God has of Himself is infinitely above the knowledge which an angel has of Him.
Reply to Objection 3. The knowledge which an angel has of God is midway between these two kinds of knowledge; nevertheless it approaches more to one of them, as was said above.
Source: Summa Theologica (New Advent)