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Induced magnetospheres form around conductive non-magnetized planetary objects (such as the ionospheres of Mars, Venus, Titan, Pluto and comets) in the electrodynamic interaction with a magnetized flowing plasma, such as the solar wind. The resulting induced currents couple the ionosphere and the deflected plasma, thus they provide insight into the solar wind’s role in powering the heating, escape and evolution of planetary atmospheres. In contrast to the analogous current systems in intrinsic magnetospheres, which were mapped decades ago at Earth, the current systems of induced magnetospheres are largely unexplored. Here, we use five years of magnetic field measurements from the Mars Atmosphere and Volatile EvolutioN (MAVEN) orbiter to empirically map the current systems of the Martian induced magnetosphere. We find unexpected features, in particular: coupling of the ionosphere and the bow shock, asymmetries between the north–south electric hemispheres and a twist in the near-Mars current system. The current flow pattern in the induced magnetosphere of Mars indicates a system driven by a magnetospheric convective electric field, powered by the solar wind interaction. Without an intrinsic magnetic field, Mars’s magnetosphere is induced by direct interaction between its atmosphere and the solar wind. The mapping of the associated current system, obtained by the MAVEN spacecraft, unveils its convective-driven nature and displays various structural differences compared to Earth.