Reconfigurable intelligent surface (RIS) with massive passive reflecting elements can greatly improve the wireless propagation environment. Although the RIS is easily introduced into the existing multiple-input multiple-output (MIMO) systems, effectively supporting MIMO technologies is still a major challenge in millimeter-wave cloud radio access networks (mmWave C-RANs) with fiber-wireless fronthaul. Herein, an optical true time delay pool-based hybrid beamforming (OTTDP-HBF) scheme, enabling centralized analog beamforming control, is proposed for the RIS-aided mmWave C-RAN. In the OTTDP-HBF scheme, the physical implementation and the computational processing of analog beamforming are decoupled from all active antenna units (AAUs) and centrally deployed. For the RIS-aided mmWave CRAN with OTTDP-HBF, we develop a two-stage precoding (TSP) algorithm, where the complex joint optimization problem of hybrid precoding matrices and the phase-shift matrix for the RIS is formulated as an alternating optimization (AO) problem and a sparse reconstruction problem. For an AAU equipped with 8 antennas, a designed example of the proposed OTTDPHBF is presented, where the performance can be significantly improved by introducing the RIS into mmWave C-RANs. Moreover, the obtained results of different schemes show that the proposed TSP algorithm is effective for the RIS-aided mmWave C-RAN with OTTDP-HBF.