Swarm robotics has garnered significant attention due to its ability to accomplish elaborate and synchronized tasks. Existing methodologies for motion planning of swarm robotic systems mainly encounter difficulties in scalability and safety guarantee. To address these limitations, we propose a Risk-aware swarm mOtion planner using conditional ValuE at Risk (ROVER) that systematically navigates large-scale swarms through cluttered environments while ensuring safety. ROVER formulates a finite-time model predictive control (FTMPC) problem predicated upon the macroscopic state of the robot swarm represented by a Gaussian Mixture Model (GMM) and integrates conditional value-at-risk (CVaR) to ensure collision avoidance. The key component of ROVER is imposing a CVaR constraint on the distribution of the Signed Distance Function between the swarm GMM and obstacles in the FTMPC to enforce collision avoidance. Utilizing the analytical expression of CVaR of a GMM derived in this work, we develop a computationally efficient solution to solve the non-linear constrained FTMPC through sequential linear programming. Simulations and comparisons with representative benchmark approaches demonstrate the effectiveness of ROVER in flexibility, scalability, and risk mitigation.