This paper proposes a memristor-assisted sign-based background calibration scheme for analog-to-digital converters (ADC). A R-2R digital-to-analog converter (DAC) was implemented with a memristor array and other peripheral circuits. The background calibration detects the error caused by DAC mismatch and corrects it by adjusting the memristor’s memristance in a feedback loop. The implemented circuit takes advantage of the memristor\'s small area and multi-state switching property. Simulation results show the feasibility of using memristors to correct mismatch in high-resolution ADC design. The proposed system has been designed in a TSMC 180nm process. Memristors will be laid on the top of the chip via Metal 5 and Metal 6.