We investigate the Oscillating Asymmetric Dark Matter (OADM) model as a potential solution to the core-cusp problem in the rotation curves of galaxies. Our analysis uses rotation curve data from 18 SPARC and 19 LITTLE THINGS galaxies selected for their high mass-to-light ratios ($>4M_\odot/L_\odot$) and reliable rotation curves. By evolving initial NFW profiles through the Boltzmann equation including late-time annihilations, we find the OADM model can successfully transform cuspy dark matter halos into core-type profiles. The best-fit parameters from our $\chi^2$ analysis for the dark matter mass range $m_\chi \in [100,1000]$ MeV yield an annihilation cross-section at the order of $\sigma/m_\chi \approx 0.06$ cm$^2$/g. These results suggest OADM annihilations could contribute to resolving the core-cusp discrepancy while remaining consistent with existing constraints. Complete details are available in our full publication.