Reconfigurable intelligent surface (RIS) has recently attracted a spurt of interest due to its innate advantages over massive MIMO on power consumption. In this paper, we study the outage performance of multi-RIS system with the help of hybrid automatic repeat request (HARQ) to improve the RIS system reliability, where the fading channels are modeled by Rician fading and the phase shift setting only depends on the line-of-sight (LoS) component. Both the exact and asymptotic outage probabilities under Type-I HARQ and HARQ with chase combining (HARQ-CC) schemes are derived. Particularly, the tractable asymptotic results empower us to derive meaningful insights for HARQ-aided multi-RIS systems. On the one hand, we find that both the Type-I and the HARQ-CC schemes can achieve full diversity that is equal to the maximal number of HARQ rounds. On the other hand, the closed-form expression of the optimal phase shift setting with respect to outage probability minimization is obtained. The optimal solution indicates that the reflecting link direction should be consistent with the direct link LoS component. Finally, the analytical results are validated by Monte-Carlo simulations.