This brief proposes a logic gate that performs a stateful OR logic operation on memristor memory. The presented logic structure concurrently executes an OR operation in the nanocrossbar architecture in a single step, which enables a fast logic operation and reduces the number of required memristors. The proposed circuit completes the in situ logic operation on the memristor memory, which alleviates the burden of the processor significantly. Through analysis and simulation, the feasibility of the OR operation is demonstrated, and the parameter optimization is analyzed.