In order to perform scale-resolving simulations of problems at industrial scale, the only affordable way forward is wall-modeled Large-Eddy Simulation (wmLES). These simulations rely on the assumption that the flow in the near-wall region only weakly depends on the core flow and can thus be modeled using universal laws derived for simpler flows, hence drastically decreasing the grid-points requirements in the boundary layer. It was shown that an algebraic wall-model based on the law of the wall, fitted using Reichardt formula gives accurate results for incompressible or weakly compressible flows. However, increasing the flow Mach number results in a significant decrease of the accuracy of such model as the compressibility effects become too important. To alleviate this issue, this work proposes a scaling of the wall-normal distance and flow velocity, before computing the wall shear-stress using Reichardt formula. When tested on adiabatic turbulent channel flows with centerline Mach numbers ranging from 0.25 to 1.5, using the Argo code developed by Cenaero and which implements a Discontinuous Galerkin method, this pre-scaling of the wall model is observed to significantly lower the error made on the mass flow-rate, maintaining it consistently around 2% as compared to the reference wall-resolved LES (wrLES). For the same cases, the unscaled wall-model leads to an increasing error with increase of the Mach number, and up to 15% at the highest Mach number. The mean velocity profile obtained when using the scaled wall model is also seen to match the reference wrLES profile quite accurately.