We present a detailed kinematic study of seven Neoarchean L-S tectonite samples in order to constrain vorticity and non-coaxial shear direction relative to foliation and elongation lineation. Samples are L-S tectonites from the Wawa Subprovince of the Archean Superior Province, more specifically the Vermilion District of NE Minnesota, a NE-trending belt of greenschist grade supracrustal rocks and granitoid bodies. Supracrustal rocks host multiple L-S tectonite packages with a well-developed sub-vertical metamorphic foliation and elongation lineation; elongation lineation generally plunges steeply to gently, although zones of shallow plunge occur locally. The Wawa Subprovince is widely interpreted as a transpressional plate margin with shear zones recording unidirectional dextral strike-slip, an interpretation held up as fundamental evidence for Archean plate-tectonic processes. However, vorticity and shear direction within Vermilion District L-S tectonites remain unconstrained. We compare data from thin-sections, X-ray computed tomography, and quartz crystallographic fabric analysis to monoclinic shear models to constrain vorticity and better understand the geometric relationships between vorticity, non-coaxial shear direction, foliation, and elongation lineation. Kinematic indicators in thin-section and image slices from X-ray computed tomography consistently record asymmetric microstructural fabrics in foliation-normal/lineation-parallel planes, whereas planes normal to foliation and elongation lineation display dominantly symmetric microstructural fabrics. Mantled porphyroclast 3D-shapes and star-volume distribution analyses indicate that porphyroclast short-axes are normal to foliation and long-axes parallel elongation lineation. Quartz crystallographic preferred orientation data show a-axes maxima sub-parallel to foliation-normal/lineation-parallel planes. Kinematic data consistently show a vorticity vector within the foliation plane and normal to elongation lineation; thus non-coaxial shear direction is sub-parallel to elongation lineation. Data are inconsistent with shear models in which non-coaxial shear direction is normal to lineation, or in which the vorticity vector is normal to foliation. Rather, kinematic data indicate that tectonites record non-coaxial shear broadly parallel to elongation lineation regardless of the geographic orientation of lineation.