Fundamentally, the issue with attempting to justify faith with reason is that you end up with effectively a cop-out.
The universe had to be created, thus we must have God, to be the creator. But who created God? I mean, if you're going to enter the realm of logic and evidence, God is a serious problem. Its effectively the same thing as an ancient Greek hearing lightning and thunder and thinking Zeus is responsible.
So yes, faith is irrational, by its very nature. It is the belief in something completely separate from any logic or evidence.
At a broad level (and I know people's particulars vary), faith in a divine being comes down to two major things:
Explain the unknowable. Same reason as the aforementioned ancient Greeks, just bumped up a few levels. We don't know, so we have to invent God to explain what we do not know. This contrasts to the scientific reasoning saying "We don't know, *yet*, but we can figure it out, eventually.
The other reasoning being is, that once you start to think about the vastness of the universe and the insignificance of the human race, one might have a tendency to despair, knowing that in all likelyhood, the universe has gotten along just fine without our whole species, and will continue just as fine when we are gone. This terrifies people at a very fundamental level, thus we get the variations on God's Plan. We are special, God as a plan for every one of us. It sounds a lot better than "There is no plan. There is no reason to exist, other than what we make for ourselves." I personally find that kind of thinking liberating, knowing that I have the theoretical freedom to do whatever I will. But I can understand why it would terrify people.
tl;dr: Yes. Faith is irrational. The moment it becomes rational, it ceases to be faith.