Complex oxide systems have attracted considerable attention because of their fascinating properties, including the magnetic ordering at the conducting interface between two band insulators, such as LaAlO3 (LAO) and SrTiO3 (STO). However, the manipulation of the spin degree of freedom at the LAO/STO heterointerface has remained elusive. Here, we have fabricated hybrid magnetic tunnel junctions consisting of Co and LAO/STO ferromagnets with the insertion of a Ti layer in between, which clearly exhibit magnetic switching and the tunnelling magnetoresistance (TMR) effect below 10 K. The magnitude and the of the TMR are strongly dependent on the direction of the rotational magnetic field parallel to the LAO/STO plane, which is attributed to a strong Rashba-type spin orbit coupling in the LAO/STO heterostructure. Our study provides a further support for the existence of the macroscopic ferromagnetism at LAO/STO heterointerfaces and opens a novel route to realize interfacial spintronics devices.