Flows in variably-saturated porous media are described by Richards' equation whose numerical solving can be troublesome and costly because of abrupt changes in the nonlinear hydraulic properties. Typically, Richards' equation exhibits sharp wetting fronts moving dynamically in the unsaturated zone while the saturated zone remains relatively smooth. In that context, local adaptation of mesh discretization (h-adaptation) or space order approximation (p-adaptation) can improve the computational efficiency. This work aims to investigate p-adaptation which is known to reach accuracy with a reduced cost compared to low-order methods. To this end, Richards' equation is solved by discontinuous Galerkin methods whose properties make them appealing for locally adaptive high-order approximation. In this study, the p-adaptative algorithm is kept simple in order to make extension to hp-adaptation as easy as possible in the future. Benefits for Richards' equation are evaluated. Results from numerical experiments demonstrate the potential of p-adaptation for Richards' equation.