We propose using the storage ring electric dipole moment (EDM) method to search for the axion dark matter induced EDM oscillation in nucleons. The method uses a combination of B and E fields to produce a resonance between the g - 2 spin precession frequency and the background axion field oscillation to greatly enhance sensitivity to it. An axion frequency range from 10(-9) Hz to 100 MHz can, in principle, be scanned with high sensitivity, corresponding to an f(a) range of 1013 GeV <= f(a) <= 10(30) GeV, the breakdown scale of the global symmetry generating the axion or axionlike particles.