The edge turbulence model Hermes (Dudson et al 2017 Plasma Phys. Control. Fusion59 05401) is set up for plasma boundary simulations with an radiofrequency (RF) antenna, using parameters characteristic of a tokamak edge. Cartesian slab geometry is used with thin plate limiters representing the ion cyclotron range of frequency (ICRF) antenna side-wall limiters. Ad-hoc DC electric biasing of the limiters, motivated by calculations with VSim (Nieter et al 2004 J. Comput. Phys.196 448), represents an induced RF sheath rectified potential in the plasma turbulence model. Flux-driven turbulence simulations demonstrate a realistic distribution of plasma profiles and fluctuations. There is a clear effect of the antenna sheath voltage leading to formation of convective cells; bias-induced convective transport flattens the scrape-off layer density profile and fluctuations penetrate into the shadow region of the limiters as the bias voltage increases. Turbulent transport for impurity ions is inferred by following ion trajectories in the simulated plasma turbulence fields, showing Bohm-like effective diffusion rates. All in all, the model elucidates the key physical phenomena governing the effects of ICRF-induced antenna biasing on the tokamak boundary plasma.