User trajectory data is becoming increasingly accessible due to the prevalence of GPS-equipped devices such as smartphones. Many existing studies focus on querying trajectories that are similar to each other in their entirety. We observe that trajectories partially similar to each other contain useful information about users' travel patterns which should not be ignored. Such partially similar trajectories are critical in applications such as epidemic contact tracing. We thus propose to query trajectories that are within a given distance range from each other for a given period of time. We formulate this problem as a sub-trajectory similarity join query named as the STS-Join. We further propose a distributed index structure and a query algorithm for STS-Join, where users retain their raw location data and only send obfuscated trajectories to a server for query processing. This helps preserve user location privacy which is vital when dealing with such data. Theoretical analysis and experiments on real data confirm the effectiveness and the efficiency of our proposed index structure and query algorithm.