Recent observational studies suggest that active region magnetic flux emerges in a twisted state and that the sense of twist depends weakly on solar hemisphere. We propose that this twist is imparted to the flux through its interaction with turbulent velocities in the convection zone. This process, designated the Sigma-effect, operates on isolated magnetic flux tubes subjected to buffeting by turbulence with a nonvanishing kinetic helicity . The Sigma-effect leads to twist of the same sense inferred from observation and opposite to that predicted by the alpha-effect. A series of numerical calculations are performed to estimate the magnitude of the Sigma-effect in the solar convective zone. The results compare favorably with observations in both mean value and statistical dispersion. We find a further relationship with total magnetic flux that can be tested in future observations. The model also predicts that twist is uncorrelated with the tilt angle of the active region.