The rapid development of Artificial Intelligence (AI) and Internet of Things (IoT) increases the requirement for edge computing with low power and relatively high processing speed devices. The Computing-In-Memory(CIM) schemes based on emerging resistive Non-Volatile Memory(NVM) show great potential in reducing the power consumption for AI computing. However, the device inconsistency of the non-volatile memory may significantly degenerate the performance of the neural network. In this paper, we propose a low power Resistive RAM (RRAM) based CIM core to not only achieve high computing efficiency but also greatly enhance the robustness by bit line regulator and bit line weight mapping algorithm. The simulation results show that the power consumption of our proposed 8-bit CIM core is only 3.61mW (256*256). The SFDR and SNDR of the CIM core achieve 59.13 dB and 46.13 dB, respectively. The proposed bit line weight mapping scheme improves the top-1 accuracy by 2.46% and 3.47% for AlexNet and VGG16 on ImageNet Large Scale Visual Recognition Competition 2012 (ILSVRC 2012) in 8-bit mode, respectively.