Rotational motions in homogeneous anisotropic elastic media are studied under the assumption of plane wave propagation. The main goal is to investigate the influences of anisotropy in the behavior of the rotational wavefield. The focus is on P-waves that theoretically do not generate rotational motion in isotropic media. By using the Kelvin–Christoffel equation, expressions are obtained of the rotational motions of body waves as a function of the propagation direction and the coefficients of the elastic modulus matrix. As a result, the amplitudes of the rotation rates and their radiation patterns are quantified and it is concluded that (1) for strong local earthquakes and typical reservoir situations quasi P-rotation rates induced by anisotropy are significant, recordable, and can be used for inverse problems; and (2) for teleseismic wavefields, anisotropic effects are unlikely to be responsible for the observed rotational energy in the P coda.