Spin and angular momenta of light are important degrees of freedom in nanophotonics which control light propagation, optical forces and information encoding. Typically, optical angular momentum is generated using q-plates or spatial light modulators. Here, we show that graphene-supported plasmonic nanostructures with broken rotational symmetry provide a surprising spin to orbital angular momentum conversion, which can be continuously controlled by changing the electrochemical potential of graphene. Upon resonant illumination by a circularly polarized plane wave, a polygonal array of indium-tin-oxide nanoparticles on a graphene sheet generates scattered field carrying electrically-tunable orbital angular momentum. This unique photonic spin-orbit coupling occurs due to the strong coupling of graphene plasmon polaritons and localised surface plasmons of the nanoparticles and leads to the controlled directional excitation of graphene plasmons. The tuneable spin-orbit conversion pave the way to high-rate information encoding in optical communications, electric steering functionalities in optical tweezers, and nanorouting of higher-dimensional entangled photon states.