The answer, according to an article in the latest issue of Political Psychology is:

In absolute terms, no way:

…Bush is definitely intelligent. The IQ estimates range between 111.1 and 138.5, with an average around 125. That places him in the upper range of college graduates in raw intellect.

Compared to other U.S. presidents, very:

Bush’s IQ is below average relative to that subset of the U.S. citizens who also managed to work their way into the White House. In fact, his intellect falls near the bottom of the distribution. When compared with twentieth-century presidents from Theodore Roosevelt through Clinton, only Harding has a lower score (at least on three of the four estimates).

I will admit, though, that for parts this article I share some of Arnold’s “junk science” worries. Many of the IQ estimates for pre-modern presidents seem pretty circular: One could easily argue that early presidents get rated as smart simply because they were political successful, and vice versa.

Hat tip to Robin Hanson.