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 and SrTiO3. However, the manipulation of the spin degree of freedom at the LaAlO3/SrTiO3 heterointerface has remained elusive. Here, we have fabricated hybrid magnetic tunnel junctions consisting of Co and LaAlO3/SrTiO3 ferromagnets with the insertion of a Ti layer in between, which clearly exhibit magnetic switching and the tunnelling magnetoresistance effect below 10 K. The magnitude and sign of the tunnelling magnetoresistance are strongly dependent on the direction of the rotational magnetic field parallel to the LaAlO3/SrTiO3 plane, which is attributed to a strong Rashba-type spin-orbit coupling in the LaAlO3/SrTiO3 heterostructure. Our study provides a further support for the existence of the macroscopic ferromagnetism at LaAlO3/SrTiO3 heterointerfaces and opens a novel route to realize interfacial spintronics devices.