Analysis of parallel genotyping and expression profiling data has shown that mRNA expression levels are highly heritable. Currently, only a tiny fraction of this genetic variance can be mechanistically accounted for. The influence of trans-acting polymorphisms on gene expression traits is often mediated by transcription factors (TFs). We present a method that exploits prior knowledge about the in vitro DNA-binding specificity of a TF in order to map the loci ('aQTLs') whose inheritance modulates its protein-level regulatory activity. Genome-wide regression of differential mRNA expression on predicted promoter affinity is used to estimate segregant-specific TF activity, which is subsequently mapped as a quantitative phenotype. In budding yeast, our method identifies six times as many locus-TF associations and more than twice as many trans-acting loci as all existing methods combined. Application to mouse data from an F2 intercross identified an aQTL on chromosome VII modulating the activity of Zscan4 in liver cells. Our method has greatly improved statistical power over existing methods, is mechanism based, strictly causal, computationally efficient, and generally applicable.