Ion and electron transport properties have been measured in a steady state, weakly turbulent plasma that was subjected to crossed E and B fields. The geometry permits quantitative measurements of electron and ion currents. The ion gyro radius is large compared to the apparatus dimensions. Measurements of the potential gradients, Hall currents, and ion velocity show that the ions are freely accelerated through the plasma by electrostatic forces. However, an ``anomalous diffusion'' of electrons is observed since the electron current across the magnetic field is much too large to be due to collisional diffusion. The plasma is weakly turbulent, consisting of a slowly rotating density concentration on which higher frequency fluctuations are superimposed. Electric field fluctuations are found that are correlated with the density variations so as to produce the ``anomalous diffusion'' via adiabatic E × B drifts. The magnitudes of these electric field and density variations are used to predict a net electron current that agrees with the direct measurements of this current. Reasonable agreement with the turbulent diffusion theory of Yoshikawa and Rose is obtained.