Cloud database services have attracted considerable interest with the increase in the amount of data to be analyzed. Delegating data management to cloud services, however, causes security and privacy issues because cloud services are not always trustable. In this study, we address the problem of answering join queries across outsourced private datasets while maintaining data confidentiality. We particularly consider a scenario in which two data owners each own a set of elements and a querier asks the cloud to perform join operations to obtain the size of the common elements in the two datasets. To process the join operations without revealing the contents of data to the cloud, we propose two protocols, a basic protocol and a querier-friendly protocol, which adopt a functionality of outsourced private set intersection cardinality (OPSI-CA) with fully homomorphic encryption (FHE) and bloom filters. The querier-friendly protocol achieves a reduction in communication and computation costs for the querier. Our experimental results show that it takes 436 s for the basic protocol and 298 s for the querier-friendly protocol to execute the join query on the two datasets with 100 elements each. The novelty of this study is that our protocols are the first approaches for outsourced join operations adopting FHE.