In this paper, we investigate the performance of RIS-aided orthogonal time frequency space (OTFS) and orthogonal frequency division multiplexing (OFDM) systems in the presence of oscillator phase noise. OFDM is known to be sensitive to phase noise, which could limit the potential gains promised by RIS systems. OTFS, on the other hand, is a compelling potential waveform for RIS-aided systems in the presence of phase noise due to it's resilience to time-varying channels. However, the effect of phase noise on OTFS has not been fully analyzed in the literature as of yet. Additionally, no existing works in the literature consider the effect of phase noise on an RIS-aided OTFS system. Hence, we propose a joint RIS channel and phase noise estimation technique using a Wiener filtering approach. Our proposed method exploits the statistical nature of both the phase noise and the Doppler spread channel in a setup with RIS. Our numerical analysis demonstrates the significant gain of RIS-aided OTFS offers compared to RIS-aided OFDM in the presence in the presence of phase noise. Additionally, our results demonstrate the superiority of our proposed estimation technique, with gains of up to 3~dB in terms of bit error rate (BER), over existing methods in the literature.