We propose a time-delayed photonic reservoir computing (RC) architecture utilizing a reflective semiconductor optical amplifier (RSOA) as an active mirror. The performance of the proposed RC structure is investigated by two benchmark tasks, namely the Santa Fe time-series prediction task and the nonlinear channel equalization task. The simulation results show that both the prediction and equalization performance of the proposed system are significantly improved with the contribution of RSOA, with respect to the traditional RC system using a mirror. By increasing the drive current of the RSOA, the greater nonlinearity of the RSOA gain saturation is achieved, as such the prediction and equalization performance are enhanced. It is also shown that the proposed RC architecture shows a wider consistency interval and superior robustness than the traditional RC structure for most of the measured parameters such as coupling strength, injection strength, and frequency detuning. This work provides a performance-enhanced time-delayed RC structure by making use of the nonlinear transformation of the RSOA feedback.