The development of multifunctional spintronic devices requires simultaneous control of multiple degrees of freedom of electrons, such as charge, spin and orbit, and especially a new physical functionality can be realized by combining two or more different physical mechanisms in one specific device. Here, we report the realization of novel tunneling rectification magnetoresistance (TRMR), where the charge-related rectification and spin-dependent tunneling magnetoresistance are integrated in Co/CoO-ZnO/Co magnetic tunneling junctions with asymmetric tunneling barriers. Moreover, by simultaneously applying direct current and alternating current to the devices, the TRMR has been remarkably tuned in the range from -300% to 2200% at low temperature. This proof-of-concept investigation provides an unexplored avenue towards electrical and magnetic control of charge and spin, which may apply to other heterojunctions to give rise to more fascinating emergent functionalities for future spintronics applications.