When I fall ill and go to the doctor, as opposed to going to medical school, is it rational? Off course it's rational. But that act of leaving my health at the hands of this dude whom the world tells me will get me back to good is essentially faith.
I'm not a very philosophical/bright type, so I may come up shot if someone wanted to take this up philosophically, but at basic level I do think faith is rational. A lot of the inputs for what we consider rational may very well be acts of faith.