Background MRI-derived cortical folding measures are an indicator of largely genetically driven early developmental processes. However, the effects of genetic risk for major mental disorders on early brain development are not well understood. Methods We extracted cortical complexity values from structural MRI data of 580 healthy participants using the CAT12 toolbox. Polygenic risk scores (PRS) for schizophrenia, bipolar disorder, major depression, and cross-disorder (incorporating cumulative genetic risk for depression, schizophrenia, bipolar disorder, autism spectrum disorder, and attention-deficit hyperactivity disorder) were computed and used in separate general linear models with cortical complexity as the regressand. In brain regions that showed a significant association between polygenic risk for mental disorders and cortical complexity, volume of interest (VOI)/region of interest (ROI) analyses were conducted to investigate additional changes in their volume and cortical thickness. Results The PRS for depression was associated with cortical complexity in the right orbitofrontal cortex (right hemisphere: p = 0.006). A subsequent VOI/ROI analysis showed no association between polygenic risk for depression and either grey matter volume or cortical thickness. We found no associations between cortical complexity and polygenic risk for either schizophrenia, bipolar disorder or psychiatric cross-disorder when correcting for multiple testing. Conclusions Changes in cortical complexity associated with polygenic risk for depression might facilitate well-established volume changes in orbitofrontal cortices in depression. Despite the absence of psychopathology, changed cortical complexity that parallels polygenic risk for depression might also change reward systems, which are also structurally affected in patients with depressive syndrome.