A reservoir computing system (RC) based on a vertical cavity surface emitting semiconductor laser (VCSEL) subject to arbitrary-polarization optical feedback is proposed, and its performance for predicting Santa-Fee time series is numerically analyzed. Taking advantage of the fact that the light emitted by VCSEL has two polarization components, a tunable polarization wave plate is placed in the feedback loop to adjust the polarization angle of the feedback light. The influences of system typical parameters on the prediction error of such a RC system have been analyzed in detail. Through optimizing the parameters of feedback strength, injection coefficient and polarization angle, the prediction error of 3% can be realized for the reservoir computing system.