The main idea behind social participatory sensing is to leverage social networks as the underlying infrastructure for recruiting social friends to participate in a sensing campaign. Such recruitment requires the transmission of messages (i.e., tasks and contributions) between the requester and participants via routes consisting of social links. When selecting the routes, the recruitment scheme should consider two fundamental factors. The first factor is the level of trustworthiness of a route, which evaluates its reliability to ensure that the integrity of the message is preserved. The second factor is the privacy level of the route, which measures information leakage in the form of disclosure of private information contained in the message by intermediate nodes. The best route will be the route with maximum credibility, i.e., highest trust score and lowest likelihood of privacy breach. In this paper, we propose a privacy-preserving trust-based recruitment framework which is aimed at finding the best route from the requester to the selected participants. We propose to quantify the privacy score of a route by utilising the concept of entropy to measure the level of privacy breach in each intermediate node along the route. The trust score of the route is obtained by multiplying the mutual trust rates of all links along the route. Simulation results demonstrate the efficacy of our framework in terms of recruiting suitable participants through the most secure and trustable routes.