In this paper, we investigate a novel multiple-input multiple-output (MIMO) radar system aided by phase shifter based polarization-reconfigurable antennas (PRAs). Specifically, a base station (BS) equipped with multiple PRAs at both the transmitter and the receiver aims to sense the unknown and random angular location parameter of a point target via sending wireless signals and processing the received echo signals reflected by the target, where only prior distribution information about the location parameter is available for exploitation. Firstly, we characterize the sensing performance of this novel PRA-based MIMO radar system by deriving the Bayesian Cramér-Rao bound (BCRB) of the mean-squared error (MSE) in estimating the desired location parameter with prior distribution information. Then, to fully exploit the new design degrees-of-freedom (DoF) empowered by PRAs, we study the joint optimization of the transmit sample covariance matrix as well as the transmit and receive phase shift vectors to minimize the sensing BCRB subject to a transmit power constraint. This problem is non-convex and difficult to solve due to the coupling among optimization variables. To resolve this issue, we develop an alternating optimization (AO) based algorithm which iteratively obtains the closed-form optimal solution to each variable with the others being fixed at each time, thus being guaranteed to converge to at least a stationary point of the joint optimization problem. Numerical results validate the effectiveness of the proposed algorithm.