We present an azimuthal-rotation-controlled dynamic nanoinscribing (ARC-DNI) process for continuous and scalable fabrication of asymmetric nanograting structures with tunable periods and shape profiles. A sliced edge of a nanograting mold, which typically has a rectangular grating profile, slides over a polymeric substrate to induce its burr-free plastic deformation into a linear nanopattern. During this continuous nanoinscribing process, the “azimuthal angle,” that is, the angle between the moving direction of the polymeric substrate and the mold’s grating line orientation, can be controlled to tailor the period, geometrical shape, and profile of the inscribed nanopatterns. By modulating the azimuthal angle, along with other important ARC-DNI parameters such as temperature, force, and inscribing speed, we demonstrate that the mold-opening profile and temperature- and time-dependent viscoelastic polymer reflow can be controlled to fabricate asymmetric, blazed, and slanted nanogratings that have diverse geometrical profiles such as trapezoidal, triangular, and parallelogrammatic. Finally, period- and profile-tunable ARC-DNI can be utilized for the practical fabrication of diverse optical devices, as is exemplified by asymmetric diffractive optical elements in this study.