Came across this book review Why Biology Is Not Destiny, which falsely claims that any physical signifiers of IQ has been debunked or discredited.
Harden is right that such assertions are controversial, but they’re nothing new. The idea of a biological hierarchy of intelligence arose alongside the first theories of human evolution. It never goes away when discredited, just changes forms. In 1810, a year after the publication of the first modern evolutionary theory, two German doctors, Franz Joseph Gall and Johann Kaspar Spurzheim, inaugurated the science of phrenology by asserting that the parts of a person’s brain reflected, by their sizes, the degrees of the person’s mental powers, and that one could evaluate these by examining the shape of the skull.
Such research was not debunked/discredited. It became politically incorrect and largely stopped. There is a positive correlation, around .4, between head size, brain volume and IQ.  Same for even the shape of the head corelating with IQ to some extent based on studies outside of the US. 
The professed consensus that such research has been ‘debunked,’ is likely attributable to Stephen J. Gould’s book The Mismeasure of Man, 1981. As it turned out, Gould committed many errors, likely ideologically motivated, as discussed here:
In The Mismeasure of Man (1981), Harvard University celebrity paleontologist Stephen J. Gould (1941-2002) critiqued IQ, the concept of race, and the evidence for race differences in IQ. In particular, Gould attacked the work of English scientist Samuel Morton (1799-1851), claiming that Morton allowed unconscious biases to influence his measurements of the supposedly differing average cranial capacities of a sample of 1,000 skulls from different races. Gould conducted his own analysis of Morton’s data and reported that, in reality, there were no consistent race differences in cranial capacity. The Mismeasure of Man publicized Gould’s findings, establishing them as the “truth” in the public mind: “No serious person,” one might say, “thinks that there are race differences in skull size—or that this would have any connection to intelligence.”
However, in 2011, researchers re-measured the cranial volumes of 46 percent of the skulls in Morton’s collection. They also re-examined the statistical analyses conducted by Morton and by Gould. They found that, in contrast to what Gould had argued, Morton had not falsified or manipulated his measurements, and to the extent that there were measurement errors in Morton’s work, they actually exaggerated African cranial capacity in comparison to European. The authors also showed that Gould had only achieved his desired cancellation of Morton by tendentiously omitting specific sub-groups of skulls and by presenting incorrect calculations.
Why does human biological diversity apply everywhere but above the neck? Somehow the human brain is supposed to be exempt from the same processes of biology that make humans unique everywhere else too, at least as it pertains to IQ (neuro-diversity, whatever that is supposed to mean, is welcomed, but intellectual diversity? no-no). The science is not settled, rather the science stopped because it became politically inconvenient. As Jordan Peterson famously said in one of his videos, if you accept other aspects of human psychology as true, such as the work of Freud and Jung, you must also accept IQ, because the science of IQ is even more statistically significant and reproducible than the science of personality traits.
In healthy individuals, intelligence is positively associated with total brain volume, with correlations ranging from 0.33 to 0.38 (Deary et al. 2010; Posthuma et al. 2002; McDaniel, 2005; Rushton and Ankney, 2009). In addition, cortical thickness of the frontal, parietal, anterior cingulate and occipital regions have been positively related to intelligence (Brans et al. 2010; Schnack et al. 2014; Colom et al. 2006; Frangou et al. 2004; Haier et al. 2004; Wilke et al. 2003). Also, higher IQ has been related to more pronounced surface contraction with increasing age, particularly in the precentral, left medial frontal and right supramarginal and parietal cortices and cuneus (Schnack et al. 2014). Although the relationship of subcortical volumes with IQ is less clear, recent findings suggest a positive relationship between thalamus volume and IQ (Bohlken et al. 2014).
Some of our results were in parallel with the thesis that “individuals who have a big brain are more intelligent.” The head breadth and skull height and IQ results were found to be positively correlated. Both measurements show the areas the brain occupies in the skull and the participants whose head breadth and skull height values were high were also found to have high IQ values. Another result of our study that morphological facial height and IQ values were negatively correlated means an increase in favor of skull height in the proportioning of skull height and morphological facial height