We propose MC-CIM, a compute-in-memory (CIM) framework for robust, yet low power, Bayesian edge intelligence. Deep neural networks (DNN) with deterministic weights cannot express their prediction uncertainties, thereby pose critical risks for applications where the consequences of mispredictions are fatal such as surgical robotics. To address this limitation, Bayesian inference of a DNN has gained attention. Using Bayesian inference, not only the prediction itself, but the prediction confidence can also be extracted for planning risk-aware actions. However, Bayesian inference of a DNN is computationally expensive, ill-suited for real-time and/or edge deployment. An approximation to Bayesian DNN using Monte Carlo Dropout (MC-Dropout) has shown high robustness along with low computational complexity. Enhancing the computational efficiency of the method, we discuss a novel CIM module that can perform in-memory probabilistic dropout in addition to in-memory weight-input scalar product to support the method. We also propose a compute-reuse reformulation of MC-Dropout where each successive instance can utilize the product-sum computations from the previous iteration. Even more, we discuss how the random instances can be optimally ordered to minimize the overall MC-Dropout workload by exploiting combinatorial optimization methods. Application of the proposed CIM-based MC-Dropout execution is discussed for MNIST character recognition and visual odometry (VO) of autonomous drones. The framework reliably gives prediction confidence amidst non-idealities imposed by MC-CIM to a good extent. Proposed MC-CIM with 16x31 SRAM array, 0.85 V supply, 16nm low-standby power (LSTP) technology consumes 27.8 pJ for 30 MC-Dropout instances of probabilistic inference in its most optimal computing and peripheral configuration, saving 43% energy compared to typical execution.