The observation of Raman scattering due to one-magnon excitation is reported for the first time on canted antiferromagnetic ErFe${\mathrm{O}}_{3}$ which has a zero-angular-momentum ground state. The magnon softening phenomenon, associated with the spin-reorientation phase transitions of this crystal, is studied through the thermal behavior of one-magnon scattering. The temperature dependence of two antiferromagnetic magnon modes is analyzed on the basis of a simple free-energy form for this spin system. Some peculiar features such as the failure of the softmode frequency to vanish at the spin-reorientation temperatures are discussed briefly. It was found that the weak ferromagnetic moment in this canted antiferromagnet must be taken into account for a satisfactory explanation of the polarization properties of the one-magnon spectra. However, the theoretical detail requires further clarification. The prominent intensity enhancement of the soft magnon line near the transition temperature is interpreted to be a result of population increase due to the mode softening associated with spin reorientation.