Harnessing active matter calls for strategies that break the directional symmetry of self-propelled motion without altering the propulsion mechanism itself. Here, we show that magnetically inert spherical active colloids can be steered through the anisotropic viscous response of a ferrofluid under a uniform magnetic field. Self-propelled Janus colloids exhibit robust cross-field motion transverse to the magnetic field, although the applied magnetic field directly controls neither the particles nor their propulsion speed. Quantitative measurements reveal an emergent reorientation torque that grows with both propulsion speed and magnetic field strength. A squirmer model in a magnetoviscous medium captures these observations and shows that the torque arises from anisotropic viscosity that couples to the swimmer-generated vorticity. Our findings establish a hydrodynamic basis for converting viscous dissipation into directional symmetry breaking through anisotropic rheology, providing a route to field-controlled material transport by active matter.