Thanks to their ability to store information in a continuous (analog) form, memristors are termed as well-suited for several real-time signal processing tasks. In this context, here we present a memristive circular buffer, using memristor and its multi-bit storage ability to temporarily store encoded information in a compact form, thus improving the area performance as well as the delay and energy consumption of the circuit, compared to conventional designs. We introduce the arithmetic encoding principles for the proposed circuit, explain the en/decoding mechanisms for the memristors-based data-management operations, and finally present the target application. For our simulation-based study we used a threshold-type device model of a bipolar voltage-controlled memristor.