Self-assembly of nanocrystals is a promising route for creating macroscale materials that derive function from the properties of their nanoscale building blocks. While much progress has been made assembling nanocrystals into different superlattices, controlling the relative orientations of nanocrystals in those lattices remains a challenge. Here, we combine experiments with computer simulations to study the self-assembly of patchy heterostructural nanocrystals (HNCs), consisting of near-spherical quantum dots decorated with regular arrangements of small gold satellites, into close-packed superlattices with pronounced orientational alignment of HNCs. Our simulations indicate that the orientational alignment is caused by van der Waals interactions between gold patches and is sensitive to the interparticle distance in the superlattice. We demonstrate experimentally that the degree and type of orientational alignment can be controlled by changing ligand populations on HNCs. This study provides guidance for the design and fabrication of nanocrystal superlattices with enhanced structural control.