Experimental nondestructive methods for probing the spatially varying arrangement and orientation of ultrastructures in hierarchical materials are in high demand. While conventional computed tomography (CT) is the method of choice for nondestructively imaging the interior of objects in three dimensions, it retrieves only scalar density fields. In addition to the traditional absorption contrast, other contrast mechanisms for image formation based on scattering and refraction are increasingly used in combination with CT methods, improving both the spatial resolution and the ability to distinguish materials of similar density. Being able to obtain vectorial information, like local growth directions and crystallite orientations, in addition to scalar density fields, is a longstanding scientific desire. In this work, it is demonstrated that, under certain conditions, the spatially varying preferred orientation of anisotropic particles embedded in a homogeneous matrix can be retrieved using CT with small-angle X-ray scattering as the contrast mechanism. Specifically, orientation maps of filler talc particles in injection-moulded isotactic polypropylene are obtained nondestructively under the key assumptions that the preferred orientation varies slowly in space and that the orientation of the flake-shaped talc particles is confined to a plane. It is expected that the method will find application inin situstudies of the mechanical deformation of composites and other materials with hierarchical structures over a range of length scales.