The axion-gluon coupling induces an oscillating electric dipole moment (EDM) in nucleons. The oscillating EDM can be detected using a storage ring EDM method with resonance between the g-2 precession and the oscillating EDM frequencies. A frequency range from mHz to 100 MHz can be scanned using the resonance method and one below mHz down to about $10^{-9}$ Hz can be searched parasitically with the frozen spin method. The estimated sensitivity is at the level of $10^{-30} \, \rm{e \cdot cm}$ or higher. No experiment has accessed the proposed frequency range at such high sensitivity until now. In this study, we present the experimental method and compare the sensitivity with other experiments. (This work was supported by IBS-R017-D1-2018-a00.)