The spin–orbit interaction (SOI) of light has been intensively studied in nanophotonics because it enables sensitive control of photons’ spin degree of freedom and thereby the trajectories of the photons, which is useful for applications such as signal encoding and routing. A recent study [Phys. Rev. Lett. 117, 166803 (2016)] showed that the SOI of photons manifests in the presence of a gradient in the permittivity of the medium through which the photons propagate; this enhances the scattering of circularly polarized light and results in the photons propagating along twisted trajectories. Here we theoretically predict that, because of the equivalence between an inhomogeneous dielectric medium and a gravitational field demonstrated in transformation optics, a significant SOI is induced onto circularly polarized light passing by the gravitational lens of a black hole. This leads to: i) the photons to propagate along chiral trajectories if the size of the black hole is smaller than the wavelength of the incident photons; ii) the resulting image of the gravitational lens to manifest an azimuthal rotation because of these chiral trajectories. The findings open for a way to probe for and discover subwavelength-size black holes using circularly polarized light.