The development of power-efficient Machine Learning Hardware is of high importance to provide Artificial Intelligence (AI) characteristics to those devices operating at the Edge. Unfortunately, state-of-the-art data-driven AI techniques such as deep learning are too costly in terms of hardware and energy requirements for Edge Computing (EC) devices. Recently, Cellular Automata (CA) have been proposed as a feasible way to implement Reservoir Computing (RC) systems in which the automaton rule is fixed and the training is performed using a linear regression model. In this work we show that Reservoir Computing based on CA may arise as a promising AI alternative for devices operating at the edge due to its intrinsic simplicity. For this purpose, a new low-power CA-based reservoir hardware is proposed and implemented in a FPGA (known as ReCA circuitry). The use of Elementary Cellular Automata (ECA) is able to further simplify the RC structure to implement a power efficient AI system suitable to be implemented in EC applications. Experiments have been conducted on the well-known MNIST handwritten digits database, obtaining competitive results in terms of processing time, circuit area, power and inference accuracy.