Free convective magnetohydrodynamic flow from a spinning vertical cone to an orthotropic Darcian porous medium under a transverse magnetic field is studied. The non-dimensionalized two-point boundary value problem is solved numerically using the Keller Box implicit finite difference method. The effects of spin parameter, orthotropic permeability functions, Prandtl number and hydromagnetic number on flow characteristics are presented graphically. Tangential velocity and swirl velocity are accentuated with increasing permeability owing to a corresponding decrease in porous media resistance. Temperatures are depressed with increasing permeability. Validation of the solutions is achieved with earlier studies. Applications of the study arise in electromagnetic spin coating materials processing. © 2017, The Brazilian Society of Mechanical Sciences and Engineering.