In light of the dynamic plasticity, nanosize, and energy efficiency of memristors, memristive reservoirs have attracted increasing attention in diverse fields of research recently. However, limited by deterministic hardware implementation, hardware reservoir adaptation is hard to realize. Existing evolutionary algorithms for evolving reservoirs are not designed for hardware implementation. They often ignore the circuit scalability and feasibility of the memristive reservoirs. In this work, based on the reconfigurable memristive units (RMUs), we first propose an evolvable memristive reservoir circuit that is capable of adaptive evolution for varying tasks, where the configuration signals of memristor are evolved directly avoiding the device variance of the memristors. Second, considering the feasibility and scalability of memristive circuits, we propose a scalable algorithm for evolving the proposed reconfigurable memristive reservoir circuit, where the reservoir circuit will not only be valid according to the circuit laws but also has the sparse topology, alleviating the scalability issue and ensuring the circuit feasibility during the evolution. Finally, we apply our proposed scalable algorithm to evolve the reconfigurable memristive reservoir circuits for a wave generation task, six prediction tasks, and one classification task. Through experiments, the feasibility and superiority of our proposed evolvable memristive reservoir circuit are demonstrated.