Stochastic fluctuations acting on a model of quasigeostrophic fluid motion on a rotating frame are shown to be rectified giving rise to large-scale noise-sustained average currents. As in other noise rectification phenomena, the effect requires nonlinearity and absence of detailed balance to occur. We apply an analytical coarse-graining procedure to obtain insight into the phenomenon. Relevance of the effect in the context of ocean modeling is briefly discussed.