The Imaginary Poynting Momentum (IPM) is associated to the imaginary part of the well-known complex Poynting vector. When light fields interact with matter, researchers usually pay attention to the real part of the complex Poynting vector, while neglect its imaginary part. However, the real Poynting vector describes only a portion of the physical mechanism underlying light-particle interaction. Recent theoretical and experimental breakthrough have been made in the study of the IPM force, which has gained increasing interest that the IPM force is independent of the optical radiation pressure and intensity gradient force. It provides a new degree of freedom for optical micromanipulation with structured light, such as vector beams, evanescent and two-wave interference fields. The IPM force can be detected directly with a Mie particle in the tightly focused Spirally Polarized Vector Beam(SPVB) when the IPM appears in the azimuthal direction. Nevertheless, the spinning optical torque caused by the vortex-like structure of IPM has not been investigated. In order to study the rotational manipulation of particles by this IPM vortex, we use the Finite-Difference Time-Domain (FDTD) method, to investigate the spinning optical torque acting on microparticles, illuminated by the SPVB, and to study the influence of the particle material properties on the torque. The cylindrical vector beam is constructed by the in-phase superposition of the radially and azimuthally polarized vector beam. When the angle of polarization is π/4, this cylindrical vector beam is the spirally polarized vector beam characterized by the IPM arising in the azimuthal direction. The FDTD method is a prevailing solution that can be used to solve Maxwell's equations and optomechanics for arbitrarily shaped particles. The scattering problem of arbitrary particles can be handled, so the FDTD method is characterized by high inclusivity and high accuracy. The spinning torque is computed rigorously based on the Maxwell stress tensor method, or the conservation of optical angular momentum of the total field. By changing the wavelength of the incident field as well as the size, shape and material of the particles, the spinning optical torque characteristics of the particles under the SPVB are analyzed comprehensively. The computation results show that this SPVB can induce the spinning optical torque, which drives the microparticle to spin about their own axis. For rod-like particles, the spinning optical torque increases first, and then decreases with the increase of incident wavelength. There is the phenomenon of resonance peaks explained by the multipole resonances induced in the particles. The spinning optical torque tends to increase first and then decrease with the increase of particle's length, and the spinning optical torque reaches the maximum value at particle's length around 2 μm. Moreover, it is found that, for the particles with complex geometrical structures (e.g., equilateral-triangle, hexagonal and chiral structures), the spinning optical torque is at least one order of magnitude larger than that of the rod-shape particle, and the values and directions of the spinning optical torques are more varied. On complex geometrically structured particles of certain sizes and materials, due to the effect of resonance, there are overall large value and opposite direction for the spinning optical torques. The particles selected in this paper have some special shapes, but for generic isotropic particles, IPM can also induce them to spin. This reveals a new method for achieving light-driven microrotors, which does not rely on the optical angular momentum. The azimuthal IPM complements the spin and orbital angular momenta in terms of their rotational mechanical effects, which has potential applications in the field of optical micromanipulation and levitated optomechanics, especially in the realization of unusual optomechanical manifestations such as the negative or left-handed optical torque.