Recommender systems (RecSys) have become an essential component of many web applications. The core of the system is a recommendation model trained on highly sensitive user-item interaction data. While privacy-enhancing techniques are actively studied in the research community, the real-world model development still depends on minimal privacy protection, e.g., via controlled access. Users of such systems should have the right to choose \emph{not} to share highly sensitive interactions. However, there is no method allowing the user to know which interactions are more sensitive than others. Thus, quantifying the privacy risk of RecSys training data is a critical step to enabling privacy-aware RecSys model development and deployment. We propose a membership-inference attack (MIA)- based privacy scoring method, RecPS, to measure privacy risks at both the interaction and user levels. The RecPS interaction-level score definition is motivated and derived from differential privacy, which is then extended to the user-level scoring method. A critical component is the interaction-level MIA method RecLiRA, which gives high-quality membership estimation. We have conducted extensive experiments on well-known benchmark datasets and RecSys models to show the unique features and benefits of RecPS scoring in risk assessment and RecSys model unlearning.