When ultralight axion dark matter encounters a static magnetic field, it sources an effective electric current that follows the magnetic field lines and oscillates at the axion Compton frequency. We propose a new experiment to detect this axion effective current. In the presence of axion dark matter, a large toroidal magnet will act like an oscillating current ring, whose induced magnetic flux can be measured by an external pickup loop inductively coupled to a SQUID magnetometer. We consider both resonant and broadband readout circuits and show that a broadband approach has advantages at small axion masses. We estimate the reach of this design, taking into account the irreducible sources of noise, and demonstrate potential sensitivity to axionlike dark matter with masses in the range of 10^{-14}-10^{-6} eV. In particular, both the broadband and resonant strategies can probe the QCD axion with a GUT-scale decay constant.