Integrating reconfigurable intelligent surface (RIS) into multi-access edge computing (MEC) systems to assist computation offloading from mobile devices (MDs) to edge servers has been increasingly considered. However, most resource allocation strategies in the current RIS-assisted MEC systems are based on perfect channel state information (CSI). Due to the passive characteristics of RIS and the large number of reflecting elements in the RIS, it is difficult to obtain the accurate CSI in RIS-assisted wireless systems. In this paper, we aim to minimize the expected energy consumption of MDs in a RIS-assisted multi-user MEC system with imperfect CSI and probabilistic latency constraints. The formulated problem is non-trivial to tackle due to the tightly coupled optimization variables, non-closed-form expression of the objective function, and the probabilistic latency constraints. To deal with the problem, we propose a constrained stochastic successive convex approximation (CSSCA) framework-based algorithm to approximate the problem into a sequence of convex surrogate problems and solve them iteratively. Extensive numerical results validate the superiority of introducing RIS into MEC systems and demonstrate that our proposed algorithm is effective when the CSI is imperfect.