In a practical multi-antenna receiver, each element of the receive antenna array has a directive antenna pattern, which is still not fully explored and investigated in academia and industry until now. When the emitter is deviated greatly from the normal direction of antenna element or is close to the null-point direction, the sensing energy by array will be seriously attenuated such that the direction-sensing performance is degraded significantly. To address such an issue, a rotatable array system is established with the directive antenna pattern of each element taken into account, where each element has the same antenna pattern. Then, the corresponding the Cramer-Rao lower bound (CRLB) is derived. Finally, a recursive rotation Root-MUSIC (RR-Root-MUSIC) direction-sensing method is proposed and its root-mean-squared-error (RMSE) performance is evaluated by the derived CRLB. Simulation results show that the proposed rotation method converges rapidly with about ten iterations, and make a significant enhancement on the direction-sensing accuracy in terms of RMSE when the target direction departs seriously far away from the normal vector of array. Compared with conventional Root-MUSIC, the sensing performance of the proposed RR-Root-MUSIC method is much closer to the CRLB.