Bound states in the continuum (BICs) allow to obtain an ultrahigh-quality-factor optical cavity. Nevertheless, BICs must be extended in one or more directions, substantially increasing the device footprint. Although super-cavity mode quasi-BICs supported by single nanopillars have been demonstrated recently, their low-quality factor and localized electromagnetic field inside the dielectric nanopillar are insufficient for high-sensitivity refractive index sensing applications. We propose a ring structure rotated by a dielectric sectorial nanostructure, which can achieve a high quality factor by breaking the rotational symmetry of the ring structure with a footprint as small as 3 µm2. As a straightforward application, we demonstrate high performance local refractive index and nanoscale film thickness sensing based on rotational symmetry breaking induced BICs. These BICs reach quality factor and sensitivity of one order of magnitude better than those of conventional super-cavity mode BICs. The proposed method provides insights into the design of compact high quality factor photonic devices, opening up new possibilities for applications in refractive index and nanoscale film thickness sensing.