In terms of if any theist can be rational, I don't think it's wise to deal in absolutes. One act alone does not make them completely irrational.
However we can look at that one act of belief in God, and ask if that is rational.
On the atheist / scientific side of things, we can say that we have evidence to suggest that the existence of God is unlikely but we cannot disprove his existence (can't prove a negative and we've yet to discover many things out there).
This leaves a margin of doubt big enough to consider the existence of God or "something" (just so happens that "God" is very popular).
Everyone, to some degree, has a want to be loved in a way that never leaves and many also have a need to have morals. Morals, may not (or don't in my opinion) come from God but since law and general society only seems to provide lawfulness, and not morals that are clearly outlined... many people find this in religion.
Also a factor is in how they grew up, their environment now. For instance, a lot of schools here in the UK, although government run (used to when I was there anyway... only 7 years ago), sung hymns, visited churches and did mostly Christian festivals. This goes a fair way to creating that feeling that this is "right", in the same way subliminal messaging works.
This coupled with things like confirmation biased and the broken clock theory in a persons (religious) experiences, lead them further down that path.
That feeling of "rightness" and their experiences, plus that gap... but them in a position where it's easy to edge their bets and believe in God.
Which then brings me on to ignorance. Not in a nasty way, I've done it myself. But if you just get fed "good news" a lot about someone, it makes it harder to believe when someone tells you the bad and you may even see the bad for yourself... but try to rationalise why they would do such bad things, because you know so much good about them.
It's human nature to do so, most people don't like to be wrong. Especially in such a big issue like religion.
So I suggest, whilst the actual evidence for the existence of God and the nature of God may suggest they aren't rational by having an opposing view. If you look at the path which lead them to their belief, it's probably not actually irrational for them to believe. That doesn't however make it the truth.