Optical angular momentum, which can realize the non-destructive and non-contact rotation control of micro-particle is of great significance to study the rotational mechanical properties of biological macromolecules, to understand the biocatalysis effect, and to reveal the mechanism of biological energy conversion. The angular momentum is comprised of spin angular momentum and orbital angular momentum. Spin angular momentum is associated with the polarization of the optical field and can cause particles to spin. Orbital angular momentum comes from the helical wave-front structure associated with the central phase singularity of the optical field and can cause particles to make circular trajectories. Normally, the orientation of the angular momentum is parallel to the optical axis (the direction in which the beam propagates), which is called the axial angular momentum. Such optical fields can induce particles to rotate around the optical axis when interacting with particles. In recent years, transverse spin angular momentum has been found in structured light fields such as evanescent, interference, and focusing field. Different from the traditional axial angular momentum, transverse spin angular momentum can drive the particle to rotate in the direction perpendicular to the optical axis, introducing a new degree of freedom for optically induced rotation technology, which is therefore expected to improve the flexibility of optically induced rotation. At present, non-axial rotation control of particles in the evanescent and interference fields have been implemented. However, the effect of transverse spin angular momentum in focusing fields still needs more attention and much deeper investigation. This paper will show some theoretical and experimental results on such an effect. A circularly polarized beam is believed to carry axial spin angular momentum. As a result, it is hard to realize transverse spinning of particles in such a beam. Nevertheless, under tight focusing, the focusing fields of such beam may carry transverse spin angular momentum. Optical vortex beams carry orbital angular momentum, and can induce orbital rotation of particles. In tightly focused vortex beams, there also exists induced spinning motion of some particles. Optical vortex beams with circular polarization carry both spin angular momentum and orbital angular momentum, and can realize non-axial spinning and orbiting motion of particles. Here, the dynamics of optically induced motion of circularly polarized vortex beams are studied. By use of T-matrix method, the optical forces and torques exerted on a particle are evaluated, and the influence of the orientation of spin angular momentum and orbital angular momentum on the non-axial spinning motion of particle is analyzed. The numerical results show that in the tightly focusing fields of circularly polarized vortex beams, the particle is trapped near the intensity maxima for orbital motion. When the direction of orbital angular momentum is the same as that of spin angular momentum, the trapped particle will experience a considerable transverse spin torque in addition to the longitudinal spin torque and the orbital torque, thus will induce a non-axial spinning of particle. When the direction of orbital angular momentum is opposite to that of spin angular momentum, the transverse spin torque will be too small to drive the non-axial spinning of particle. Finally, the holographic optical tweezers system has been applied to experimentally investigate the complex motion forms of the light-induced rotation in the focusing fields of circularly polarized vortex beams. The experimental results show that the direction of orbiting motion of trapped microparticle is determined by the sign of the topological charge of the vortex beam. And when the orbital angular momentum and the spin angular momentum in the circularly polarized beams have the same direction, the trapped microparticle orbits around the optical axis while, but also experiences a non-axial spinning motion. The experimental results agreed well with the theoretical results.