The bio-inspired engineering of tissue equivalents should take into account anisotropic morphology and the mechanical properties of the extracellular matrix. This especially applies to collagen fibrils, which have various, but highly defined, orientations throughout tissues and organs. There are several methods available to control the alignment of soluble collagen monomers, but the options to direct native insoluble collagen fibers are limited. Here we apply a controlled counter-rotating cone extrusion technology to engineer tubular collagen constructs with defined anisotropy. Driven by diverging inner and outer cone rotation speeds, collagen fibrils from bovine skin were extruded and precipitated onto mandrels as tubes with oriented fibers and bundles, as examined by second harmonic generation microscopy and quantitative image analysis. A clear correlation was found whereby the direction and extent of collagen fiber alignment during extrusion were a function of the shear forces caused by a combination of the cone rotation and flow direction. A gradual change in the fiber direction, spanning +50 to −40°, was observed throughout the sections of the sample, with an average decrease ranging from 2.3 to 2.6° every 10 μm. By varying the cone speeds, the collagen constructs showed differences in elasticity and toughness, spanning 900–2000 kPa and 19–35 mJ, respectively. Rotational extrusion presents an enabling technology to create and control the (an)isotropic architecture of collagen constructs for application in tissue engineering and regenerative medicine.