The amount of data stored in data repositories increases every year. This makes it challenging to link records between different datasets across companies and even internally, while adhering to privacy regulations. Address or name changes, and even different spelling used for entity data, can prevent companies from using private deduplication or record-linking solutions such as private set intersection (PSI). To this end, we propose a new and efficient privacy-preserving record linkage (PPRL) protocol that combines PSI and local sensitive hash (LSH) functions, and runs in linear time. We explain the privacy guarantees that our protocol provides and demonstrate its practicality by executing the protocol over two datasets with $2^{20}$ records each, in $11-45$ minutes, depending on network settings.