The nuclear spin resonance of 181Ta in a single crystal of KTaO3 has been studied using the technique of direct ultrasonic excitation. Nuclear resonances have been observed for transitions where ∆m=+/-1 and +/-2, where m is the magnetic quantum number. Longitudinal and both polarizations of transverse waves, set up along the  axis of the cubic crystal, were used to excite the nuclear spin resonances. The interaction which leads to the absorption of energy by the nuclear spins from the externally generated phonons is via the torque exerted on the nuclear electric quadrupole moment by the dynamic electric field gradient created by the passage of the sound wave. Expressions for the ultrasonic absorption by the nuclear spins are presented, and the predictions of the angular dependence of the resonant intensity are compared with experiment. The agreement between theory and experiment is found to be fair, and possible reasons for the discrepancy are suggested.