We report the interaction between non-spherical swimmers and a long-standing flow structure, Lagrangian coherent structures (LCSs), in a weakly turbulent two-dimensional flow. Using a hybrid experimental-numerical model, we show that rod-like swimmers have a much stronger and more robust preferential alignment with attracting LCSs than with repelling LCSs. Tracing the swimmers’ Lagrangian trajectories, we reveal that the preferential alignment is the consequence of the competition between the intrinsic mobility of the swimmers and the reorientation ability of the strain rate near the attracting LCSs. The strong preferential alignment with attracting LCSs further leads to a strong clustering near the attracting LCSs. Moreover, we show the self-similarity of this clustering, which reduces the intricate interaction to only one control parameter. Our results generically elucidate the interaction between active and non-spherical swimmers with LCSs and, thus, can be widely applied to many natural and engineered fluids including ocean flow.