Recently, resistive-based neural networks have been adopted to build deep learning architectures, where the small area footprint RRAMs (memristors) enables unprecedentedly large neural networks. In this work, we introduce a current sensing circuit and an integrated activation function for resistive neural networks for the first time. This circuit is vital since it is replicated hundreds of times at the outputs of the neurons and thus should be low power and ultra-compact. The proposed circuit is designed using TSMC65nm. The circuit is based on the current conveyor principle and a simple inverter to create the required activation function. The obtained response is curve-fitted to hyperbolic tangent and sigmoid functions to get the accurate expression for the nonlinear function used to design the training technique of the entire neural network. Finally, the proposed circuit is tested in a four-bit neural network based ADC.