In this paper, we explore the integration of two revolutionary technologies, reconfigurable intelligent surfaces (RISs) and orthogonal time frequency space (OTFS) modulation, to enhance high-speed wireless communications. We introduce a novel phase shift design algorithm for RIS-assisted OTFS, optimizing energy reception and channel gain in dynamic environments. The study evaluates the proposed approach in a downlink scenario, demonstrating significant performance improvements compared to benchmark schemes in the literature, particularly in terms of bit error rate (BER). Our results showcase the potential of RIS to enhance the system's performance. Specifically, our proposed phase shift design technique outperforms the benchmark solutions by over 4 dB. Furthermore, even greater gains can be obtained as the number of RIS elements increases.