DNA pattern matching is a key technique applied in many bioinformatics applications. Recently, this technique has become very popular and is widely used for genetic disease diagnosis, where finding the number of consecutive repeats of a specific DNA pattern indicates the type and intensity of the patient's disorder. However, the remarkable growth of DNA data exacerbates the latency and power consumption required to perform DNA pattern matching. In this work, we propose a hardware accelerator design to detect the presence of different diseases efficiently using DNA pattern matching. We propose a novel CAM cell using binary memristors for reliable and robust data encoding. The proposed architecture consists of two main building blocks the Content-addressable memory (CAM) and pattern detector circuits in addition to the needed peripheral circuits for CAM read, write and match operation. We implement and simulate the full architecture using PTM 45nm technology. The evaluation of the proposed design shows around 2x improvement in the energy-delay-area product compared to the state-of-art work in the literature, in addition to robustness against noise and process variations.