In the past decade, some telescopes (e.g. Fermi-LAT, AMS and DAMPE) were launched to detect the signals of annihilating dark matter in our Galaxy. Although some excess of gamma rays, anti-protons and electrons/positrons have been reported and claimed as dark matter signals, the uncertainties of Galactic pulsars’ contributions are still too large to confirm the claims. In this article, we report a possible radio signal of annihilating dark matter manifested in the archival radio continuum spectral data of the Abell 4038 cluster. By assuming the thermal annihilation cross section and comparing the dark matter annihilation model with the null hypothesis (cosmic ray emission without dark matter annihilation), we get very large Test Statistic values TS >45 for four popular annihilation channels, which correspond to more than 6σ statistical preference. This reveals a possible potential signal of annihilating dark matter. In particular, our results are also consistent with the recent claims of dark matter mass m ≈ 30 − 50 GeV annihilating via the $b\bar{b}$ quark channel with the thermal annihilation cross section. However, we cannot, at this time, exclude the possibility that a better background cosmic-ray model could explain the spectral data without recourse to dark matter annihilations.