Motivated by the ubiquity of natural particles in turbulent flows in the natural environment as well as in many industrial processes, we investigate statistics of rotational motion of small, inertialess triaxial ellipsoids in homogeneous isotropic turbulence. The results are obtained from integrating equations of motion along Lagrangian trajectories from direct numerical simulations data. The total particle angular velocity and its components along all three principal axes of the particle are considered. The variance of the particle angular velocity, commonly referred to as particle enstrophy, is found to show a small increase as particles become elongated. However, for particles of all shapes, the majority of the particle enstrophy is found to be in rotations about the longest axis. The results further reveal that rotations that result in a full revolution of the particle occur only due to rare events. We attempt explain these results by considering the contributions of vorticity and strain-rate to particle rotation.