The human subcortex is involved in memory and cognition. Structural and functional changes in subcortical regions is implicated in psychiatric conditions. We performed an association study of subcortical volumes using 15,941 tandem repeats (TRs) derived from whole exome sequencing (WES) data in 16,527 unrelated European ancestry participants. We identified 17 loci, most of which were associated with accumbens volume, and nine of which had fine-mapping probability supporting their causal effect on subcortical volume independent of surrounding variation. The most significant association involvedNTN1-[GCGG]Nand increased accumbens volume (β=5.93, P=8.16x10-9). Three exonic TRs had large effects on thalamus volume (LAT2-[CATC]Nβ=-949, P=3.84x10-6andSLC39A4-[CAG]Nβ=-1599, P=2.42x10-8) and pallidum volume (MCM2-[AGG]Nβ=-404.9, P=147x10-7). These genetic effects were consistent measurements of per-repeat expansion/contraction effects on organism fitness. With 3-dimensional modeling, we reinforced these effects to show that the expanded and contractedLAT2-[CATC]Nrepeat causes a frameshift mutation that prevents appropriate protein folding. These TRs also exhibited independent effects on several psychiatric symptoms, includingLAT2-[CATC]Nand the tiredness/low energy symptom of depression (β=0.340, P=0.003). These findings link genetic variation to tractable biology in the brain and relevant psychiatric symptoms. We also chart one pathway for TR prioritization in future complex trait genetic studies.