We report rectification spectroscopy (RS) for single molecules performed with continuous-wave terahertz (CW THz) radiation at the tunneling junction of a scanning tunneling microscope (STM) at 8 K. CW THz-RS serves as a new technique in single-molecule vibrational and magnetic excitation spectroscopy besides inelastic electron tunneling spectroscopy (IETS). By quantitatively studying IETS and THz RS, we show that CW THz induces a sinusoidal bias modulation with amplitude linearly dependent on the THz far-field amplitude. Such THz-induced bias modulation amplitude appears to be sensitive to the THz beam alignment but insensitive to variation in the tunneling gap far smaller than the THz wavelength.