Physical-layer key generation (PKG) exploits the reciprocity and randomness of wireless channels to generate a symmetric key between two legitimate communication ends. However, in multi-cell systems, PKG suffers from severe pilot contamination due to the reuse of pilots in different cells. In this paper, we invoke multiple reconfigurable intelligent surfaces (RISs) for adaptively shaping the environment and enhancing the PKG performance. To this end, we formulate an optimization problem to maximize the weighted sum key rate (WSKR) by jointly optimizing the precoding matrices at the base stations (BSs) and the phase shifts at the RISs. For addressing the non-convexity of the problem, we derive an upper bound of the WSKR and prove its tightness. To tackle the upper bound maximization problem, we apply an alternating optimization (AO)-based algorithm to divide the joint optimization into two sub-problems. We apply the Lagrangian dual approach based on the Karush-Kuhn-Tucker (KKT) conditions for the sub-problem of precoding matrices and adopt a projected gradient ascent (PGA) algorithm for the sub-problem of phase shifts. Simulation results confirm the near-optimal performance of the proposed algorithm and the effectiveness of RISs for improving the WSKR via mitigating pilot contamination.