The answer is, and must be, that it depends.
Aquinas, as one might expect, considers the matter explicitly. His response is not so much that faith is a virtue, however, but that faith can be a virtue, if certain conditions are met. If those conditions are not met, however, it is not a virtue, although it may at times be virtuous.
Faith is a pretty broad term; there are people who don't like the fact that it's as broad as it is (because of the religious associations of the word they like to pretend that they hold nothing on faith) but it's just plain fact that it is, and has always been. One can, for instance, call it faith when one accepts a conclusion on the basis of premises that don't rule out all alternatives. Faith in this sense is the result of probable arguments of any sort; the category of mental dispositions and acts this describes has no particular or typical relation to the good, and thus is not a reasonable candidate for a virtue. There is no special virtue to mere belief as such. It does not follow, of course, that there are no relevant virtues; a particular case of belief could belong to the virtue of prudence, or of fortitude, or of justice, or of any other virtue to which belief can be at all relevant. Such virtues set up what we might call presumptions for reasonable and unreasonable belief: if you have a friend, it may well be unjust to believe a particular claim about him if you don't have very strong evidence, and it may well be that the just thing requires the sort of belief that falls under the category of faith given the probabilities. And, of course, faith on the basis of authority, which is faith in a narrower and more proper sense, is simply a subspecies of faith on the basis of probability.
Faith as such cannot be a virtue at all unless certain Christian doctrines are true. As the Christian understands faith, it can fit the definition of a virtue because it can have some sort of reliable inclination to the true and the good. In order to have this reliable inclination it must be formed by charity; as it has traditionally been put, faith is a virtue only if it is a living faith. And the faith in question has to be faith in the First Truth. Thus the Christian can make sense of faith as such being a virtue, but it depends crucially on Christian belief: that there is First Truth, namely, God, and that divine Truth is presented as authoritative for belief, and also that that this disposition is informed by the sort of charity made possible by grace. There is a sharp distinction between the acquired faith mentioned above and this infused faith.
I think there is room to worry when people try to make it a virtue of itself outside of this very precise context, which seems to have become very common in certain circles. As I said above, particular cases could belong to other kinds of virtues, depending on circumstances, but acquired faith is too diverse a category to be a virtue in its own right. There is no reliable inclination of any sort to the true and the good -- some cases will hit and some will miss. The person who takes acquired faith to be an acquired virtue is doing violence to prudence; he is attributing to acquired faith characteristics that are really just usurped from theological faith. If Christian doctrine is true, there is a real virtue of faith; it does not follow from this that all faith is this virtue of faith.
