We demonstrate a frequency-agile terahertz wave parametric oscillator (TPO) in a ring-cavity configuration (ring-TPO). The TPO consists of three mirrors and a MgO:LiNbO(3) crystal under noncollinear phase-matching conditions. A novel, fast frequency-tuning method was realized by controlling a mirror of the three-mirror ring cavity. The wide tuning range between 0.93 and 2.7 THz was accomplished. For first demonstration using the ring-TPO, terahertz spectroscopy was performed as the verification of the frequency-agile performance, measuring the transmission spectrum of the monosaccharide glucose. The spectrum was obtained within about 8 s in good comparison to those of Fourier transform infrared spectrometer.