In this study, we present a topological transport theory–the turbulence pinch in magnetized plasmas–by utilizing the generalized Kelvin's circulation as a constraint. An exact nonlinear relation between the Kelvin's circulation pinch velocity and the turbulence vorticity flux has been derived. The flux-driven feature of the circulation pinch suggests an approach to non-locally control particle pinch velocity through varying boundary conditions. Due to its ubiquity and robustness, this theory provides a promising mechanism to produce an up-gradient particle transport.