The strain in hybrid van der Waals heterostructures, made of two distinct two-dimensional van der Waals materials, offers an interesting handle on their corresponding electronic band structure. Such strain can be engineered by changing the relative crystallographic orientation between the constitutive monolayers, notably, the angular misorientation, also known as the “twist angle”. By combining angle-resolved photoemission spectroscopy with density functional theory calculations, we investigate here the band structure of the WS2/graphene heterobilayer for various twist angles. Despite the relatively weak coupling between WS2 and graphene, we demonstrate that the resulting strain quantitatively affects many electronic features of the WS2 monolayers, including the spin-orbit coupling strength. In particular, we show that the WS2 spin-orbit splitting of the valence band maximum at K can be tuned from 430 to 460 meV. Our findings open perspectives in controlling the band dispersion of van der Waals materials.