In this article we explore Ni/HfO2/TiN resistive random access memory (RRAM) as ultralow power synaptic element in deep neural networks (DNN) for artificial intelligence applications. Low power RRAM devices are fabricated and measured, with very low RESET current and 2-3 orders of resistance window. The SET-RESET current-voltage characteristics, high-and low-resistance state statistical distribution, and analog programming characteristics are calibrated to analytical models. Training and inference for the MNIST handwritten digits dataset using a multilayer perceptron was simulated based on the calibrated model using CIMulator, a novel neuromorphic simulation platform for compute-in-memory circuitry to predict DNN inference accuracy and energy consumption. Despite larger inherent device-to-device variability due to low on current, 97% inference accuracy is achieved with only 2-bit for the weights using weight update accumulation technique.