One technology that has the potential to improve wireless communications in years to come is integrated sensing and communication (ISAC). In this study, we take advantage of reconfigurable intelligent surface's (RIS) potential advantages to achieve ISAC while using the same frequency and resources. Specifically, by using the reflecting elements, the RIS dynamically modifies the radio waves' strength or phase in order to change the environment for radio transmission and increase the ISAC systems' transmission rate. We investigate a single cell downlink communication situation with RIS assistance. Combining the ISAC base station's (BS) beamforming with RIS's discrete phase shift optimization, while guaranteeing the sensing signal, The aim of optimizing the sum rate is specified. We take advantage of alternating maximization to find practical solutions with dividing the challenge into two minor issues. The first power allocation subproblem is non-convex that CVX solves by converting it to convex. A local search strategy is used to solve the second subproblem of phase shift optimization. According to the results of the simulation, using RIS with adjusted phase shifts can significantly enhance the ISAC system's performance.