AbstractArbitrary polarized vortex beam induced by polarization singularity offers a new platform for both classical optics and quantum entanglement applications. Bound states in the continuum (BICs) have been demonstrated to be associated with topological charge and vortex polarization singularities in momentum space. For conventional symmetric photonic crystal slabs (PhCSs), BIC is enclosed by linearly polarized far fields with winding angle of 2π, which is unfavorable for high-capacity and multi-functionality integration-optics applications. Here, we show that by breaking σ_z-symmetry of the PhCS, asymmetry in upward and downward directions and arbitrarily polarized BIC can be realized with a bilayer-twisted PhCS. It exhibits elliptical polarization states with constant ellipticity angle at every point in momentum space within the vicinity of BIC. The topological nature of BIC reflects on the orientation angle of polarization state, with a topological charge of 1 for any value of ellipticity angle. Full coverage of Poincaré sphere (i.e., $- {{π \over 4}} \le χ \le {{π \over 4}}$ − π 4 ≤ χ ≤ π 4 and $- {{π \over 2}} \le ψ \le {{π \over 2}}$ − π 2 ≤ ψ ≤ π 2 ) and higher-order Poincaré sphere can be realized by tailoring the twist angles. Our findings may open up new avenues for applications in structured light, quantum optics, and twistronics for photons.