We demonstrate acoustic trapping in both position and orientation of a non-spherical particle of sub-wavelength size in mid-air. To do so, we multiplex in time a pseudo-one-dimensional vertical standing wave and a twin-trap; the vertical standing wave provides converging forces that trap in position, whereas the twin-trap applies a stabilising torque that locks the orientation. The device operates at 40 kHz, and the employed multiplexing ratio of the 2 acoustic fields is 100:50 (standing:twin) periods. This ratio can be changed to provide tunability of the relative trapping strength and converging torque. The torsional spring stiffness of the trap is measured through simulations and experiments with good agreement. Cubes from λ/5.56 (1.5 mm) to λ/2.5 (3.4 mm) side length were stably locked. We also apply this technique to lock different non-spherical particles in mid-air: cubes, pyramids, cylinders, and insects such as flies and crickets. This technique adds significant functionality to mid-air acoustic levitation and will enable applications in micro-scale manufacturing as well as containment of specimens for examination and 3D-scanning.