Integrated sensing and communication (ISAC) systems are typically deployed in multipath environments, which is usually deemed as a challenging issue for wireless communications. However, the multipath propagation can also provide extra illumination and observation perspectives for radar sensing, which offers spatial diversity gain for detecting targets with spatial radar cross-section (RCS) fluctuations. In this letter, we propose to utilize reconfigurable intelligent surfaces (RIS) in ISAC systems to provide high-quality and controllable multipath propagation for improving the performance of fluctuating target detection and simultaneously enhancing the quality of communication services. To effectively exploit the spatial diversity offered by RIS-empowered multipath, the dual-functional transmit beamforming and the RIS reflection beamforming are jointly designed to maximize the expectation of radar signal-to-noise ratio (SNR). To solve the resulting complex non-convex optimization problem, we develop an efficient alternating optimization algorithm that utilizes majorization-minimization (MM) and alternating direction method of multipliers (ADMM) algorithms. Simulation results illustrate the advantages of multipath exploitation and the proposed beamforming design algorithm for fluctuating target detection in RIS-assisted ISAC systems.