Can faith be rational? I think this depends on what you mean by the word "rational." If, in order for a belief to be rational, I must have reasons for the belief, then faith is, by definition, not rational. And in that sense, fideism specifically recommends that one not be rational. The question, then, is whether this is a very good notion about rationality.
It is possible, in at least some cases, to be rational in holding a belief even though one has no reasons for the belief. I think that very many beliefs require reasons in order to be rational. But there are some beliefs which do not require reasons in order to be rational.
So is religious faith rational? That depends on whether, indeed, reasons to believe in God are required for that belief to be rational. Now, some recent philosophers, most prominently the American William Alston, have argued that belief in God is a "basic belief" -- in other words, faith can be rational even though it is not supported by reasons. How can Alston say that? Well, he says that some people have certain religious experiences, in which they can, as it were, perceive that God exists, or they can feel God's presence. And just like belief that you feel the pain, you don't need reasons to believe that you are experiencing God's existence when you feel his presence. So Alston is fairly called a moderate mystic, in the sense I defined earlier. Here's the idea. Suppose you think you can come into some sort of immediate contact with God -- you think you feel God's presence. Then the idea is that you don't have to have reasons to believe that you feel God's presence. The belief, that you do indeed feel God's presence, is nevertheless rational. You have what might be called "rational faith." That, at least roughly put, is Alston's sort of view.
If you think you feel God's presence, then you already believe in God. You may not have realized it, but you do. One does not feel the presence of something one knows not to exist. The rational reasons for believing in God without evidence of Its existence are economic and social advantage. Most people either accept what mommy and daddy told them or switch to a religion that offers a better deal.
Now needless to say, if you don't believe you have such experiences, or if you think that these experiences are just a kind of vivid imagination, then you won't be at all impressed by Alston's view. And then you will maintain that, if belief in God is to be rational, it must be supported by reasons. In other words, if you disagree with Alston, you will maintain that the belief in God is in that large class of beliefs which do require reasons in order to be rational. That doesn't mean that you will necessarily be an agnostic or an atheist. You could still be a theist. You'd simply maintain that you do have evidence or reasons to believe that God exists.
So what if you think about all this, and come to a conclusion, saying, "Alston is wrong; we can't simply say, without any reasons, that we can feel the presence of God in nature and in our lives, and then expect to be rational in our belief in God. Belief in God has to be backed up by arguments in order to be rational. Blind faith, is irrational; and so fideism recommends irrationality. But I don't care about rationality. Or rather, I want to be rational when it comes to my career, my family, and so forth; but when it comes to religious life, rationality is not a virtue. So, even if faith is irrational, that doesn't matter. In fact, it might be a virtue to believe in God irrationally! My very irrationality would show my devotion to God!"
It is not at all clear that it is possible to compartmentalize your life, so that you say that irrationality is all right in religious matters, but not in more ordinary matters. If you permit yourself to be irrational in religious matters, you will also, under excitement or duress, permit yourself to be irrational in non-religious matters.