To what extent does AFQT correlate with IQ?
An answer is found in an official memo, albeit from 1980, where


the correlation of AFQT with WAIS (no version specified) was stated as 0.8 based on a Army "fact sheet" from 1965; the details of the comparative test could not be found
an Air Force comparison found (in 1974) that the correlation (again with WAIS, no version specified) for white enlistees was (again) 0.8 but 0.77 for black enlistees.


(This ~0.8 is actually about the same as the correlation of IQ tests with SAT.) I don't know if the AFQT is still the same as back then.

A official-looking 2006 concordance/translation table of AFQT score with SAT scores can also be found, although it's rather summary; it doesn't mention a correlation coefficient.