Antiferromagnetic resonance in a bulk α-MnTe crystal is investigated using both frequency-domain and time-domain THz spectroscopy techniques. At low temperatures, an excitation at the photon energy of (3.5± 0.1)~meV is observed and identified as a magnon mode through its distinctive dependence on temperature and magnetic field. This behavior is reproduced using a simplified model for antiferromagnetic resonance in an easy-plane antiferromagnet. The results of our experiments, when compared to exchange constants established in the literature, allow us to extract the out-of-plane component of the single-ion magnetic anisotropy reaching (40±10)~μeV.