In axion models, interactions between axions and electromagnetic waves induce frequency-dependent time delays determined by the axion mass and decay constant. These small delays are difficult to detect, limiting the effectiveness of traditional methods. We compute such delays under realistic radio telescope conditions and identify a prominent dispersive feature near half the axion mass, which appears nondivergent within the limits of observational resolution. Based on this, we develop a machine learning method that achieves 90% classification accuracy and demonstrates performance well in low signal-to-noise regimes. The method's robustness is confirmed against false positives using both simulated noisy data and real-world, known-null observations. Future improvements in optical clock precision and telescope bandwidth, particularly with instruments such as the Qitai Radio Telescope, may enhance constraints on the axion decay constant by up to 4 orders of magnitude in the 10-6 similar to 10-4 eV mass range.