This paper studies integrated sensing and communication (ISAC) technology in a full-duplex (FD) uplink communication system. As opposed to the half-duplex system, where sensing is conducted in a first-emit-then-listen manner, FD ISAC system emits and listens simultaneously and hence conducts uninterrupted target sensing. Besides, impressed by the recently emerging reconfigurable intelligent surface (RIS) technology, we also employ RIS to improve the self-interference (SI) suppression and signal processing gain. As will be seen, the joint beamforming, RIS configuration and mobile users' power allocation is a difficult optimization problem. To resolve this challenge, via leveraging the cutting-the-edge majorization-minimization (MM) and penalty-dual-decomposition (PDD) methods, we develop an iterative solution that optimizes all variables via using convex optimization techniques. Numerical results demonstrate the effectiveness of our proposed solution and the great benefit of employing RIS in the FD ISAC system.