As a companion work to our previous study [F. Xu, , Phys. Rev. E. 75, 026613 (2007)] on radiation force prediction for a homogeneous spheroid, we provide in this paper the analytical solution to the radiation torque exerted by an arbitrarily shaped beam on a spheroid, which can be prolate or oblate, transparent or absorbing. Calculations based upon this theoretical development are performed for both linearly and circularly polarized incident beams, and the results are compared to those of a sphere. Stable orientations of spheroids inside a linearly and a circularly polarized Gaussian beam are predicted. We analyze two physical mechanisms, the polarization torque and the reaction force torque, which do not exist or have no contribution to the torque on a sphere but cause rotation of a spheroid. As verification, the dipole method is also developed for the torque calculation for spheroids of size much less than the wavelength, and geometrical optics is developed to qualitatively analyze the torque exerted on spheroids of large size.