Do Republicans have a lower IQ than Democrats?

The short answer is no. The slightly longer answer is that I would highly doubt the statistical significance of the popular "studies" you can find online. Furthermore, intelligence is more a function of using collected knowledge effectively and various other forms of connecting the dots, for lack of a better term. Intelligence has more to do with how the individual came to have the specific party affiliations or beliefs rather than the affiliations/beliefs themselves. 

Democrats, as a whole, are less educated an amass less wealth.  To me, that means they aren't as smart, but that's just me.

Not HS Grad              College Grad & Post-grad
% of Democrats            32%                           15%
% of Independents       22%                           18%
% of Republicans          19%                           23%

Here is the data on people who earn incomes over $75,000 which is also highly correlated to IQ:

                        Income under $75,000        over $75,000
% of Democrats            74%                             26%
% of Independents        72%                             28%
% of Republicans           57%                             43%