Perchlorate Reclamation and Water Replenishment Act This bill amends the Reclamation Wastewater and Groundwater Study and Facilities Act to authorize the Bureau of Reclamation to provide financial assistance to local water authorities for perchlorate remediation projects in areas identified by the Bureau, the Army Corps of Engineers, or a state designating agency as having experienced an impact from perchlorate contamination to: (1) design and construct water replenishment and reclamation projects that are owned and operated by the local water authority, or (2) operate and maintain such projects. The bill defines an "eligible project" as one that enhances the resilience of domestic water supplies through: on site and off site treatment facilities, on site and off site reclamation facilities, recycled water facilities and associated distribution facilities, and/or groundwater wells and associated distribution facilities. The Bureau shall give priority to projects that serve an area: (1) that has received federal authorization for projects associated with perchlorate contamination remediation programs under the Bureau or the Corps of Engineers, (2) for which a feasibility study for perchlorate remediation efforts that is acceptable to the Bureau or the Corps of Engineers has been completed, or (3) where the regional water agency that imports out-of-basin water supplies has a wholesale area that includes a population of not more than 350,000. The federal share shall not exceed 25% of the total cost of such a project.