This work presents a hybrid CMOS-RRAM integration of spiking nonvolatile computing-in-memory (nvCIM) processing engine (PE) that includes a 64Kb RRAM macro and a novel in situ nonlinear activation (ISNA) module. We integrate the computing controller and nonlinear activation function on-chip to compute convolutional or fully-connected neural network. ISNA merges A/D conversion and activation computation by leveraging its nonlinear working region. This eliminates the need for additional circuits to realize nonlinearity and reduces area by 43.7x w.r.t. the ADC scheme. The activation precision of ISNA can be configured from 1 to 8 bits to balance throughput, accuracy and power efficiency. The measurement of 4-layer LeNet shows such optimization improves 23.1% of computing speed via compromising a 2.5% relative accuracy drop. The proposed nvCIM PE achieves 16.9 TOPS/W power efficiency and a maximum spike frequency of 99.24 MHz.