Volcanic arcs at convergent plate margins are primary surface expressions of plate tectonics. Although climate affects many of the manifestations of plate tectonics via erosion, the upwelling of magmas and location of volcanic arcs are considered insensitive to climate. In the Southern Andes, subduction of the Nazca oceanic plate below the South American continent generates the Southern Andes Volcanic zone. Orographic interactions with Pacific westerlies lead to high precipitation and erosion on the western slopes of the belt between 42-46°S. At these latitudes, the topographic water divide and the volcanic arc are respectively farther and closer to the subduction trench than at lower latitudes, despite a constant subduction dip angle along strike. Here, we use thermomechanical numerical modeling to investigate how magma upwelling is affected by topographic changes due to orography. We show that a leeward topographic shift may entail a windward asymmetry of crustal structures accommodating the magma upwelling, consistent with the observed trench-ward migration of the Southern Andes Volcanic Zone. A climatic control on the location of volcanic arcs via orography and erosion is thus revealed.