Blaise Pascal, who I consider a rational agent, said:
The prophecies, the very miracles and proofs of our religion, are not of such a nature that they can be said to be absolutely convincing. But they are also of such a kind that it cannot be said that it is unreasonable to believe them. Thus there is both evidence and obscurity to enlighten some and confuse others.
Therefore, his view of the Christian scriptures is that a rational agent could reasonably believe or disbelieve the "proofs of our religion". This is also the view of Alvin Plantinga and it seems the authors of the Bible as well.
Other religions, particularly Islam, believe that their scripture is self-validating:
Surely, any sincere and unbiased searcher of truth will come to believe that the Qur'an is the revealed Book of Allah.
Here's an example of the argument:
"The above observation makes the hypothesis advanced by those who see Muhammad as the author of the Qur'an untenable. How could a man, from being illiterate, become the most important author, in terms of literary merits, in the whole of Arabic literature? How could he then pronounce truths of a scientific nature that no other human being could possibly have developed at that time, and all this without once making the slightest error in his pronouncement on the subject?"
Maurice Bucaille, THE BIBLE, THE QUR'AN AND SCIENCE, 1978, p. 125.
I don't have any particular evidence that people who believe these sorts of statements are not rational beings. My personal experience with people who make these claims is that they are rational. It would be unfair of me to claim they are irrational so that I can dismiss their claims as irrational.
I believe that I am a rational agent. I believe the Christian scriptures were "breathed out by God", which doesn't quite mean they were written by God, but that they were directly inspired by him. This isn't really the time or place to defend that belief, but the basic outline looks like this:
1) The Bible, when it treats historical subjects, broadly reflects historical reality.
2) The historical events treated by the Bible, particularly in the life and death of Jesus, are strong evidence of a God not anticipated or invented by humanity.
3) History since the events of the Bible shows rational men and women clinging to their belief in the truth of the Bible even to the point of death.
I don't expect anyone to be persuaded by this sort of argument (point #1 would probably be impossible to prove to someone who firmly rejects the Bible), but I would hope other rational agents could imagine how I might rationally be convinced of this.
Update: To answer JDH's comment, there are essentially two questions that I see: the explicit and the implied. The answer to the explicit question seems to be "No". (Other answers bare that out, I believe.) For the Bible, at least, there's even an expectation that it will be seen as foolish:
For Jews demand signs and Greeks seek wisdom, but we preach Christ crucified, a stumbling block to Jews and folly to Gentiles, but to those who are called, both Jews and Greeks, Christ the power of God and the wisdom of God. -- 1 Corinthians 1:22-24 (ESV)
That's a restatement of the first section above.
But there is also an implied question: "If there's nothing that can written in a text that would convince a rational person that it was written by a god, can a rational person believe a text was written by a god?" It is a question of what Dr. Plantinga calls Warrant which loosely defined is that property that separates knowledge from belief. One might extrapolate that since evidence for god-inspired texts isn't absolutely convincing, that belief in god-inspired texts isn't warranted.
I pointed out in the second section, that some do hold that some holy texts are self-validating, but you can't dismiss the claim out of hand. The specific evidence for the claim must be dealt with. It would be invalid to hold that people who believe a particular text is god-inspired can be written off as arational agents. I think the evidence for the Qur'an is a bit thin, but until I deal with it directly, I can't say that belief in its god-inspired status is unwarranted. That would be an invalid shortcut.
The third section deals with my personal belief. I'd be happy to defend it1, but it would be time-consuming and of perhaps limited interest. Even though I feel the evidence is strong, I know that each step would be hotly contested and at the end of the day, my view would be rejected by some (and probably all who don't already agree with me). But the point is the evidence itself must be evaluated, not the person making the claim.
- I've started my defense of the first point about the historical reliably at the Skeptics site.