Soft robots hold promise for well-matched interactions with delicate objects, humans and unstructured environments owing to their intrinsic material compliance. Movement and stiffness modulation, which is challenging yet needed for an effective demonstration, can be devised by drawing inspiration from plants. Plants use a coordinated and reversible modulation of intracellular turgor (pressure) to tune their stiffness and achieve macroscopic movements. Plant-inspired osmotic actuation was recently proposed, yet reversibility is still an open issue hampering its implementation, also in soft robotics. Here we show a reversible osmotic actuation strategy based on the electrosorption of ions on flexible porous carbon electrodes driven at low input voltages (1.3 V). We demonstrate reversible stiffening (~5-fold increase) and actuation (~500 deg rotation) of a tendril-like soft robot (diameter ~1 mm). Our approach highlights the potential of plant-inspired technologies for developing soft robots based on biocompatible materials and safe voltages making them appealing for prospective applications.