Integrated sensing and communication (ISAC), assisted by reconfigurable intelligent surface (RIS) has emerged as a breakthrough technology to improve the capacity and reliability of 6G wireless network. However, a significant challenge in RIS-ISAC systems is the acquisition of channel state information (CSI), largely due to co-channel interference, which hinders meeting the required reliability standards. To address this issue, a minimax-concave penalty (MCP)-based CSI refinement scheme is proposed. This approach utilizes an element-grouping strategy to jointly estimate the ISAC channel and the RIS phase shift matrix. Unlike previous methods, our scheme exploits the inherent sparsity in RIS-assisted ISAC channels to reduce training overhead, and the near-optimal solution is derived for our studied RIS-ISAC scheme. The effectiveness of the element-grouping strategy is validated through simulation experiments, demonstrating superior channel estimation results when compared to existing benchmarks.