Non-spherical particles are common in colloidal science. Spheroidal shapes are particularly convenient for the analysis of the pertinent electrostatic and hydrodynamic problems and are thus widely used to model the manipulation of biological cells as well as deformed drops and bubbles. We study the rotary motion of a dielectric spheroidal micro-particle which is freely suspended in an unbounded electrolyte solution in the presence of a uniform applied electric field, assuming a thin Debye layer. For the common case of a uniform distribution of the native surface-charge density, the rotary motion of the particle is generated by the contributions of the induced-charge electro-osmotic (ICEO) slip and the dielectrophoresis associated with the distribution of the Maxwell stress, respectively. Series solutions are obtained by using spheroidal (prolate or oblate) coordinates. Explicit results are presented for the angular velocity of particles spanning the entire spectrum from rod-like to disk-like shapes. These results demonstrate the non-monotonic variation of the angular speed with the eccentricity of particle shape and the singularity of the multiple limits corresponding to conducting (ideally polarizable) particles of extreme eccentricity (e ≈ 1). The non-monotonic variation of the angular speed with the particle dielectric permittivity is related to the induced-charge contribution. We apply these results to describe the motion of particles subject to a uniform field rotating in the plane. For a sufficiently slow rotation rate, prolate particles eventually become "locked" to the external field with their stationary relative orientation in the plane of rotation being determined by the particle eccentricity and dielectric constant. This effect may be of potential use in the manipulation of poly-disperse suspensions of dielectric non-spherical particles. Oblate spheroids invariably approach a uniform orientation with their symmetry axes directed normal to the external-field plane of rotation.