I was having an argument with a religious friend of mine and I told him that I didn't think I could argue with him anymore because his belief in God was irrational. He replied that my belief in reason was irrational. Is belief in reason irrational?

You friend is reviving a delightful argument from Sextus Empiricus (Outlines of Pyrrhonism) to the effect that any justification of the value of rational proof has to be either a rational proof and hence circular, or irrational and hence inconsistent with the conclusion one is trying to establish! It is a devilish argument. While it does show that you can't justify the use of rational argument from nowhere, it doesn't show that there can't be strong pragmatic reasons for using rational argument that do not consist in proofs that it is justifiable. The very fact that it is a deeply embedded and successful practice may make it prima facie justified, with the burden of proof for one who wishes to dislodge it on the other's shoulders. Note that critiques of rational argument are equally question-begging. Wittgenstein's ON CERTAINTY is a nice source for a subtle discussion of this issue.