We investigate the effect of the twist angle on the proximity spin-orbit coupling (SOC) in graphene/NbSe2 heterostructures from first principles. The low-energy Dirac bands of several different commensurate twisted supercells are fitted to a model Hamiltonian, allowing us to study the twist-angle dependency of the SOC in detail. We predict that the magnitude of the Rashba SOC can triple, when going from Θ=0° to Θ=30° twist angle. Furthermore, at a twist angle of Θ≈23° the in-plane spin texture acquires a large radial component, corresponding to a Rashba angle of up to Φ=25°. The twist-angle dependence of the extracted proximity SOC is explained by analyzing the orbital decomposition of the Dirac states to reveal with which NbSe2 bands they hybridize strongest. Finally, we employ a Kubo formula to evaluate the efficiency of conventional and unconventional charge-to-spin conversion in the studied heterostructures.