We report on the switching of the in-plane magnetization of thin yttrium iron garnet (YIG)/Pt bilayers induced by an electrical current. The switching is either field-induced and assisted by a dc current, or current-induced and assisted by a static magnetic field. The reversal of the magnetization occurs at a current density as low as $10^5$~A/cm$^{2}$ and magnetic fields of $sim 40$~$mu$T, two orders of magnitude smaller than in ferromagnetic metals, consistently with the weak uniaxial anisotropy of the YIG layers. We use the transverse component of the spin Hall magnetoresistance to sense the magnetic orientation of YIG while sweeping the current. Our measurements and simulations reveal that the current-induced effective field responsible for switching is due to the Oersted field generated by the current flowing in the Pt layer rather than by spin-orbit torques, and that the switching efficiency is influenced by pinning of the magnetic domains.
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