kappa-(BEDT-TTF)(2)I-3 is an electronically extreme two-dimensional organic metal with a superconducting transition at around 4 K. In magnetic fields above 12 T the effective mass, as obtained from the temperature dependence of the amplitudes of Shubnikov-de Haas oscillations, is magnetic field dependent as long as the magnetic field is arranged perpendicular to the conducting planes. In contrast to this, by turning the magnetic field by 27 degrees or even only 9 degrees the observed effective mass (as obtained from Shubnikov-de Haas and de Haas-van Alphen measurements) is field independent. We suppose that the occurrence of anyons at temperatures below 1 K in fields above 12 T is the reason for the observed field dependence of the effective mass.