The plasmon-enhanced spin and orbital rotation of Au dimer, two optically bound nanoparticles (NPs), induced by a circularly polarized (CP) light (plane wave or Gaussian beam) were studied theoretically. Through the optomechanical performances of optical forces and torques, the longitudinal/transverse spin-orbit coupling (SOC) of twisted electromagnetic fields was investigated. The optical forces show that for the long-range interaction, there exist some stable-equilibrium orbits for rotation, where the stable-equilibrium interparticle distances are nearly the integer multiples of wavelength in medium. In addition, the optical spin torque drives each NP to spin individually. For a plane wave, the helicities of the longitudinal spin and orbital rotation of the coupled NPs are the same at the stable-equilibrium orbit, consistent with the handedness of plane wave. In contrast, for a focused Gaussian beam, the helicity of the orbital rotation of dimer could be opposite to the handedness of the incident light due to the negative optical orbital torque at the stable-equilibrium interparticle distance; additionally, the transverse spin of each NP becomes profound. These results demonstrate that the longitudinal/transverse SOC is significantly induced due to the twisted optical field. For the short-range interaction, the mutual attraction between two NPs is induced, associated with the spinning and spiral trajectory; eventually, the two NPs will collide. The borderline of the interparticle distance between the long-range and short-range interactions is approximately at a half-wavelength in medium.