Objection 1. It would seem that faith does not reside in the intellect. For Augustine says (De Praedest. Sanct. v) that "faith resides in the believer's will." Now the will is a power distinct from the intellect. Therefore faith does not reside in the intellect.
Objection 2. Further, the assent of faith to believe anything, proceeds from the will obeying God. Therefore it seems that faith owes all its praise to obedience. Now obedience is in the will. Therefore faith is in the will, and not in the intellect.
Objection 3. Further, the intellect is either speculative or practical. Now faith is not in the speculative intellect, since this is not concerned with things to be sought or avoided, as stated in De Anima iii, 9, so that it is not a principle of operation, whereas "faith... worketh by charity" (Galatians 5:6). Likewise, neither is it in the practical intellect, the object of which is some true, contingent thing, that can be made or done. For the object of faith is the Eternal Truth, as was shown above (Question 1, Article 1). Therefore faith does not reside in the intellect.
On the contrary, Faith is succeeded by the heavenly vision, according to 1 Corinthians 13:12: "We see now through a glass in a dark manner; but then face to face." Now vision is in the intellect. Therefore faith is likewise.
I answer that, Since faith is a virtue, its act must needs be perfect. Now, for the perfection of an act proceeding from two active principles, each of these principles must be perfect: for it is not possible for a thing to be sawn well, unless the sawyer possess the art, and the saw be well fitted for sawing. Now, in a power of the soul, which is related to opposite objects, a disposition to act well is a habit, as stated above (I-II, 49, 4, ad 1,2,3). Wherefore an act that proceeds from two such powers must be perfected by a habit residing in each of them. Again, it has been stated above (2, 1,2) that to believe is an act of the intellect inasmuch as the will moves it to assent. And this act proceeds from the will and the intellect, both of which have a natural aptitude to be perfected in this way. Consequently, if the act of faith is to be perfect, there needs to be a habit in the will as well as in the intellect: even as there needs to be the habit of prudence in the reason, besides the habit of temperance in the concupiscible faculty, in order that the act of that faculty be perfect. Now, to believe is immediately an act of the intellect, because the object of that act is "the true," which pertains properly to the intellect. Consequently faith, which is the proper principle of that act, must needs reside in the intellect.
Reply to Objection 1. Augustine takes faith for the act of faith, which is described as depending on the believer's will, in so far as his intellect assents to matters of faith at the command of the will.
Reply to Objection 2. Not only does the will need to be ready to obey but also the intellect needs to be well disposed to follow the command of the will, even as the concupiscible faculty needs to be well disposed in order to follow the command of reason; hence there needs to be a habit of virtue not only in the commanding will but also in the assenting intellect.
Reply to Objection 3. Faith resides in the speculative intellect, as evidenced by its object. But since this object, which is the First Truth, is the end of all our desires and actions, as Augustine proves (De Trin. i, 8), it follows that faith worketh by charity just as "the speculative intellect becomes practical by extension" (De Anima iii, 10).
Source: Summa Theologica (New Advent)