Most type practitioners avoid discussing the relationship between type and I.Q. because they assume that people can't deal with the truth. Unfortunately, the silence of the experts has led to rampant speculation instead of fact-based discussion. The internet is full of arrogant type bigots and people with crushed self esteem who either believe their type is particularly smart or particularly dumb. However, they are both wrong.
We do not know if type is related to intelligence. However, type is related to your ability to score high on an I.Q., SAT, or ACT test. Here's the rub: intelligence is not precisely the same thing as a high I.Q. score.
You probably think I'm just being politically correct, but no, I'm an INTP. Are we known for that? ;p Let's get real here: it may still be unknown whether type is related to intelligence, but you can use an I.Q. test instead of the Myers-Briggs to figure out a person's type preferences. I.Q. tests measure abstract reasoning skill (Intuition), the ability to solve problems alone and silently within your head (Introversion), the ability to think objectively about non-people oriented problems (Thinking), and flexibility in solving never-before-seen problems (Perceiving). There is no fresh news here; all of this is predicted by type theory.
And indeed, the more of those preferences you have, the higher your score on an I.Q. test is likely to be. Introverts tend to do better than Extraverts. Intuitives tend to do better than Sensors. Thinkers are slightly preferred over Feelers. Perceivers have an advantage over Judgers. These are average trends, of course, but they all add up to a clear ranking based on personality characteristics.
For this reason, INTPs are predicted to do the best of all types on I.Q. tests. Does this mean they are more intelligent than average? We don't know. But we do know that the very format of the test introduces confounding factors that give INTPs a leg up on everybody else. Not to say that I.Q. tests are completely worthless (read on) but there are strong type-based biases that may result in junk data.
Now. Culturally speaking--I deal in stereotypes--the INTP personality is considered the very epitomy of intelligence. People reason thus: Einstein was an INTP; Einstein was a genius; INTPs act like Einstein; therefore every INTP is a genius. (Flawlessly logical.)
Now, what happens to someone like Mozart, the Artisan child prodigy who couldn't have looked less like Einstein? Mozart was a frightently brilliant guy, but his brilliance would have been shortchanged by our current I.Q. tests, which measure type as well as genuine intelligence.
In fact, type strongly determines how intelligence is expressed. An Artisan genius won't work math problems; they will make music. An Idealist genius won't make music, they will write literature. For example, an NF child genius may have somewhat above average math ability, but college level poetry comprehension ability. Mozart may have been able to compose original music at age 5, but that doesn't make him "smart" by Einstein's INTP standards. Yet Mozart clearly had a unique, powerful Artisan mind.
An I.Q. test does accurately measure intelligence for certain types--mainly INs, and to a lesser extent all Intuitives. For Introverted Intuitives alone, an I.Q. test is more or less fair, and can be put to valid use for comparative purposes. An INTP with an I.Q. of 150 is really smarter than an INTP with an I.Q. of 140, provided that both INTPs have the same levels of Introversion, Intuition, Thinking, and Perceiving rather than being borderline on one of the preferences. But an I.Q. test cannot tell you whether an INTP with an I.Q. of 150 is smarter than an ESFJ with an I.Q. of 140, because the inherent bias of the test renders the data invalid for ESFJs. Essentially, most Sensing types cannot be tested because the confounding factors are too strong to permit real intertype comparisons. (Intuition is the biggy, since I.Q. tests are extremely abstract.) In fact, I would go so far as to say that I.Q. tests do not constitute valid data on intelligence for most non-INs, though there are ENP types that also score very highly.
Okay, so now that we've beaten that horse into a pulp, you're probably curious as to where INTPs fall in the I.Q. ranking. All the factors are in their favor, so they should be the highest ranked type.
Three I.Q. studies have placed INTPs between 2nd and 6th place out of 16 types (McCaulley & Kainz, 1976; McCaulley & Natter, 1974; Myers in Myers & McCaulley, 1985). This is close to what we would expect based on our hypothesis above--a nearly top-ranked score. The amount of variability is normal.
Remember that no two INTPs are alike either in terms of type or intelligence. The discussion above is of averages and generalities; you may be above or below average compared to the rest of your type.