Conventional photocurrents at a p-n junction depend on macroscopic built-in fields and are typically insensitive to the microscopic details of a crystal's atomic configuration. Here we demonstrate how atomic configuration can control photocurrent in van der Waals (vdW) heterostructures. In particular, we find bulk shift photocurrents (SPC) in vdW heterostructures display a rich (atomic) configuration dependent phenomenology that range from contrasting SPC currents for different stacking arrangements (e.g., AB vs BA stacking) to a strong light polarization dependence for SPC that align with crystallographic axes in a vdW heterostructure. Strikingly, we find that SPC in vdW heterostructures can be directed by modest strain, yielding sizeable photocurrent magnitudes under unpolarized light irradiation and manifesting even in the absence of p-n junctions. These demonstrate that SPC are intimately linked to how the Bloch wavefunctions in a vdW heterostructure are embedded in real space, and enables a new macroscopic transport probe (photocurrent) of lattice-scale registration in vdW materials.