Free space optical (FSO) communications offer high speed, low cost, and strong anti-interference ability. However, the atmospheric turbulence-induced fading causes deterioration in the performance of FSO communication systems. The conventional solution is to use RF links as parallel communication links to improve the system performance. On the other hand, reconfigurable intelligent surfaces (RIS) can be employed to further improve the received signal-to-noise ratio of the RF link due to its advantages of low loss, easy deployment, and no complex coding and decoding. In this paper, an RIS-assisted hybrid RF-FSO transmission system is proposed to improve the communication quality of service. Based on this hybrid model, exact expressions for the outage probability, average BER, and channel capacity are derived, and Monte-Carlo simulations are presented to verify the accuracy of the analytical results. Results show that the performance of the proposed system is significantly improved compared to the conventional hybrid RF-FSO system.