We report electrical current switching of noncollinear antiferromagnetic (AFM) Mn$_3$GaN/Pt bilayers at room temperature. The Hall resistance of these bilayers can be manipulated by applying a pulse current of $1.5times10^6$~A/cm$^2$, whereas no significant change is observed up to $sim10^8$~A/cm$^2$ in Mn$_3$GaN single films, indicating that the Pt layer plays an important role. In comparison with ferrimagnetic Mn$_3$GaN/Pt bilayers, a lower electrical current switching of noncollinear AFM Mn$_3$GaN is demonstrated, with a critical current density two orders of magnitude smaller. Our results highlight that a combination of a noncollinear AFM antiperovskite nitride and a spin-torque technique is a good platform of AFM spintronics.