  We theoretically study the proximity spin-orbit coupling in graphene on
transition-metal dichalcogenides monolayer stacked with arbitrary twist angles.
We find that the relative rotation greatly enhances the spin splitting of
graphene, typically by a few to ten times compared to the non-rotated
geometry,and the maximum splitting is achieved around $20^\circ$. The induced
SOC can be changed from the Zeeman-type to the Rashba-type by rotation. The
spin-splitting is also quite sensitive to the gate-induced potential, and it
sharply rises when the graphene's Dirac point is shifted toward the TMDC band.
The theoretical method does not need the exact lattice matching and it is
applicable to any incommensurate bilayer systems. It is useful for the
twist-angle engineering of a variety of van der Waals proximity effects.

Mesoscale and Nanoscale Physics