Two-dimensional (2D) perovskites are an emerging class of layered materials with unique optoelectronic properties. To date, most 2D perovskites with Ruddlesden-Popper (RP) phase reported are organic- inorganic hybrid perovskites with long organic spacers. Here, we report a high-quality all-inorganic 2D perovskite, Cs2PbI2Cl2, synthesized by an aqueous method. The as-synthesized perovskite crystals exhibit large in-plane emission and reflection optical anisotropy. The maximum in-plane linear dichroic ratio is up to 9.6 for exciton emission and 2.0 for reflection at 77 K. The large in-plane optical anisotropy may be ascribed to the strong electron-phonon interaction-induced lattice distortion. The large optical anisotropy enables us to construct a polarization-sensitive photodetector based on this perovskite, for which the linear dichroic ratio of photoresponse is about 1.2. Our study provides an alternative avenue to achieve in-plane optical anisotropy in an isotropy structure and thus would be of great importance for polarization-associated applications.