Fluidic rectification refers to anisotropic flow resistance upon changing the flow direction. Polymeric solutions, in contrast to Newtonian fluids, can exhibit an anisotropic flow resistance in microfluidic devices by tuning the channel shape at low Reynolds number. Such a concept has not been investigated in an anisotropic porous medium. We have developed a fluidic rectifier based on an anisotropic porous medium consisting of a periodic array of triangular pillars that can operate at a low Reynolds number. Rectification is achieved, when the type of high Weissenberg number elastic instabilities changes with the flow direction. The flow resistance differs across the two directions of the anisotropic porous medium geometry. We have identified the type of elastic instabilities that appear in both forward and backward directions. Particularly, we found a qualitative relation between the dead-zone instability and the onset of fluidic rectification.