The support vector regression (SVR) algorithm is presented to demodulate the torsion angle of an optical fiber torsion sensor based on the Sagnac interferometer with the panda fiber. Experimental results demonstrate that with the aid of SVR algorithm, the information in the transmission spectrum of the sensor can be used fully to realize the regression prediction of the directional torsion angle. The full torsion angle ranges from -360° to 360° can be predicted with a mean absolute error (MAE) of 2.24° and determination coefficient (R2) of 0.9996. The impact of the angle sampling interval and wavelength resolution of the spectrometer on the prediction accuracy of the directional torsion angle and the suitability of the SVR algorithm for compact optical fiber sensor and other optical fiber torsion sensors based on the Sagnac interferometer are discussed. Moreover, the multi-objective SVR algorithm is used to eliminate the interference of strain during torsion angle measurement. The SVR algorithm can efficiently enlarge the measurement range of the torsion angle and break through the challenge of demodulating sensing signal for compact fiber torsion sensor. Compared to the prediction accuracy of common machine learning algorithms of artificial neural network (ANN) algorithm, random forest (RF) algorithm, and K-nearest neighbor (KNN) algorithm, the SVR algorithm has the advantages of higher measurement accuracy and shorter testing time.