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The paper presents a method of measuring the angle of rotation and twist using a tilted fibre Bragg grating (TFBG) periodic structure with a tilt angle of 6◦, written into a single-mode optical fibre. It has been shown that the rotation of the sensor by 180◦ causes a change in the transmission coefficient from 0.5 to 0.84 at a wavelength of 1541.2 nm. As a result of measurements it was determined that the highest sensitivity can be obtained for angles from 30◦ to 70◦ in relation to the basic orientation. The change in the transmission spectrum occurs for cladding modes that change their intensity with the change in the polarization of light propagating through the grating. The same structure can also be used to measure the twist angle. The possibility of obtaining a TFBG twist by 200◦ over a length of 10 mm has been proved. This makes it possible to monitor both the angle of rotation and the twist of an optical fibre with the fabricated TFBG.