We study the current-induced torques in asymmetric magnetic tunnel junctions containing a conventional ferromagnet and a magnetic Weyl semimetal contact. The Weyl semimetal hosts chiral bulk states and topologically protected Fermi arc surface states which were found to govern the voltage behavior and efficiency of current-induced torques. We report how bulk chirality dictates the sign of the non-equilibrium torques acting on the ferromagnet and discuss the existence of large field-like torques acting on the magnetic Weyl semimetal which exceeds the theoretical maximum of conventional magnetic tunnel junctions. The latter are derived from the Fermi arc spin texture and display a counter-intuitive dependence on the Weyl nodes separation. Our results shed light on the new physics of multilayered spintronic devices comprising of magnetic Weyl semimetals, which might open doors for new energy efficient spintronic devices.