The flow gradient tensor controls the rate of dissipation of concentration fluctuations due to local dispersion, and therefore determines the rate of dilution of solute in a spatially random flow field. Off-diagonal terms of the flow gradient tensor quantify the rotational characteristics of the flow. A leading order description of the vorticity (omega = (omega(1), omega(2), omega(3))), of flow in a three-dimensionally random spatially correlated hydraulic conductivity field (K(x)) is made by relating the vorticity spectrum to the spectrum of ln K(x). Distinct components of the vorticity are found to be linearly uncorrelated (<(omega(i) omega(j))over bar> = 0, i not equal j). The characteristic vorticity component in the bulk flow direction is zero (sigma(omega 1) = 0), and the characteristic vorticity in the transverse directions (sigma(omega 2), sigma(omega 3)) are inversely proportional to the hydraulic conductivity microscales in the other transverse direction, as exhibited in a numerical calculation of the vorticity.