Objection 1. It would seem that the demons have no faith. For Augustine says (De Praedest. Sanct. v) that "faith depends on the believer's will": and this is a good will, since by it man wishes to believe in God. Since then no deliberate will of the demons is good, as stated above (I, 64, 2, ad 5), it seems that in the demons there is no faith.
Objection 2. Further, faith is a gift of Divine grace, according to Ephesians 2:8: "By grace you are saved through faith... for it is the gift of God." Now, according to a gloss on Hosea 3:1, "They look to strange gods, and love the husks of the grapes," the demons lost their gifts of grace by sinning. Therefore faith did not remain in the demons after they sinned.
Objection 3. Further, unbelief would seem to be graver than other sins, as Augustine observes (Tract. lxxxix in Joan.) on John 15:22, "If I had not come and spoken to them, they would not have sin: but now they have no excuse for their sin." Now the sin of unbelief is in some men. Consequently, if the demons have faith, some men would be guilty of a sin graver than that of the demons, which seems unreasonable. Therefore in the demons there is no faith.
On the contrary, It is written (James 2:19): "The devils... believe and tremble."
I answer that, As stated above (1, 4; 2, 1), the believer's intellect assents to that which he believes, not because he sees it either in itself, or by resolving it to first self-evident principles, but because his will commands his intellect to assent. Now, that the will moves the intellect to assent, may be due to two causes. First, through the will being directed to the good, and in this way, to believe is a praiseworthy action. Secondly, because the intellect is convinced that it ought to believe what is said, though that conviction is not based on objective evidence. Thus if a prophet, while preaching the word of God, were to foretell something, and were to give a sign, by raising a dead person to life, the intellect of a witness would be convinced so as to recognize clearly that God, Who lieth not, was speaking, although the thing itself foretold would not be evident in itself, and consequently the essence of faith would not be removed.
Accordingly we must say that faith is commended in the first sense in the faithful of Christ: and in this way faith is not in the demons, but only in the second way, for they see many evident signs, whereby they recognize that the teaching of the Church is from God, although they do not see the things themselves that the Church teaches, for instance that there are three Persons in God, and so forth.
Reply to Objection 1. The demons are, in a way, compelled to believe, by the evidence of signs, and so their will deserves no praise for their belief.
Reply to Objection 2. Faith, which is a gift of grace, inclines man to believe, by giving him a certain affection for the good, even when that faith is lifeless. Consequently the faith which the demons have, is not a gift of grace. Rather are they compelled to believe through their natural intellectual acumen.
Reply to Objection 3. The very fact that the signs of faith are so evident, that the demons are compelled to believe, is displeasing to them, so that their malice is by no means diminished by their believe.
Source: Summa Theologica (New Advent)