A novel method to implement distributed fiber optic Brillouin sensing was proposed, using the frequency shifting technique via a Brillouin fiber optic ring cavity. The method is based on the Brillouin optical time-domain analysis (BOTDA) principle that a laser beam from single-longitudinal model lasing is divided into two beams; one beam is launched into the Brillouin fiber optic ring cavity to generate the stimulated Brillouin scattering wave of narrow bandwidth as the Stokes wave, the other one is taken as the pump wave through phase modulation at a low frequency; the Stokes and the pump waves counter-propagate along the sensing fiber optic and the Brillouin frequency spectrum is measured to get the temperature or strain in fiber optic. The proposed method translates a microwave frequency signal into a MHz frequency signal for detection and processing with only one laser. The system is simple in structure with low cost and can eliminate the impact of the laser frequency fluctuation on the measurement precision. Experiments show that the method is feasibe.