The flow of an electrically conducting fluid in a thin disc under the action of an azimuthal Lorentz force is studied experimentally. At small forcing, the Lorentz force is balanced by either viscosity or inertia, yielding quasi-Keplerian velocity profiles. For very large current I and moderate magnetic field B, we observe a new regime, fully turbulent, which exhibits large fluctuations and a Keplerian mean rotation profile , where r is the distance from the axis. In this turbulent regime, the dynamics is typical of thin layer turbulence, characterized by a direct cascade of energy towards the small scales and an inverse cascade to large scales. Finally, at very large magnetic field, this turbulent flow bifurcates to a quasi-bidimensional turbulent flow involving the formation of a large scale condensate in the horizontal plane. These results are well understood as resulting from an instability of the Bödewadt–Hartmann layers at large Reynolds number and discussed in the framework of similar astrophysical flows.