Many analog circuit design optimization problems involve performing expensive simulations to evaluate circuit configurations in terms of multiple objectives and constraints; Oftentimes, practitioners have preferences over objectives. We aim to approximate the optimal Pareto set over feasible circuit configurations by minimizing the number of simulations. We propose a novel and efficient preference-aware constrained multi-objective Bayesian optimization (PAC-MOO) approach that learns surrogate models for objectives and constraints and sequentially selects candidate circuits for simulation that maximize the information gained about the optimal constrained Pareto-front while factoring in the objective preferences. Our experiments on real-world problems demonstrate PAC-MOO's efficacy over prior methods.