The evidence is contradictory and does not appear to be uniform internationally or over time.
In the United States, at this moment, people with more education tend to be more socially liberal, while not necessarily favoring more economic regulation. And, more intelligent people tend to be more partisan. But, education is not a perfect proxy for intelligence, and this has not always been the case.
Studies in Britain and Brazil found that people who were more intelligent favored more moderate political parties.
In the U.S., in contrast, a lot of "unaffiliated" voters, who are sometimes characterized as ideologically "moderate", actually do not have coherent political ideologies, are easily swayed from one stance to another depending upon how it is presented or who is presenting it, and are more influenced in their political decision making by the personalities of the candidates and by referendum style decision making (i.e. voting the bums out when your personal circumstances are less good, and keeping incumbents when your personal circumstances are favorable).
The difference may have something to do with the fact that the U.S. has only two viable political parties, with many people who aren't strongly partisan simply having never thought seriously about politics; they are, instead, largely apolitical. But, in Britain and Brazil there are multiple electorally viable parties to choose from, and choosing a moderate one is a choice that calls for more nuance which calls for greater intelligence.
Also, the voting and ideological preferences of more educated voters in the United States have shifted significantly in the last fifty years or so, in part, as part of a general process called "realignment" in which the policies and demographics associated with particular political parties has almost completely flipped the role of the Democratic and Republican political parties. Since political identification is often fixed as a young adult, this transitional phase has led to an incoherent set of associations for the electorate as a whole.
For example, many older people who identify as Christian and conservative Republican in the Northeastern United States did so when that identification was much more centrist than it is today.
A 2010 study did find that people in the U.S. who identified as libertarian at that time had higher IQ than those who identified as liberal or conservative, but some of that is a function of the comparisons not really being apples to apples. Lots of less educated people who have basically libertarian views don't self-identify as libertarian because they have never heard of the term. But, there aren't great instruments to distinguish between liberals with coherent political ideologies, relative to people who have vaguely liberal ideas but no really clearly articulated or considered political ideology.
A self-identification as libertarian implies that one has had the leisure and inclination to develop an overarching personal political theory, in a way that identification as liberal or conservative does not. In much the same way, someone who has given religious issues enough serious thought to self-identify as atheist or agnostic will have a higher IQ, on average, than someone who merely identifies as "non-religious" and has never given religious issues much serious consideration.