The nonlinear interaction of ultrasonic waves with a nonspherical particle may give rise to the acoustic radiation torque on the particle. This phenomenon is investigated here considering a rigid prolate spheroidal particle of subwavelength dimensions that is much smaller than the wavelength. Using the partial wave expansion in spheroidal coordinates, the radiation torque of a traveling and standing plane wave with arbitrary orientation is exactly derived in the dipole approximation. We obtain asymptotic expressions of the torque as the particle geometry approaches a sphere and a straight line. As the particle is trapped in a pressure node of a standing plane wave, its radiation torque equals that of a traveling plane wave. We also find how the torque changes with the particle aspect ratio. Our findings are in excellent agreement with previous numerical computations. Also, by analyzing the torque potential energy, we determine the stable and unstable spatial configuration available for a particle.
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