The two-dimensional Ruddlesden-Popper (RP) phases are an important class of halide perovskites with versatile optoelectronic properties. So far, only organic-inorganic hybrid RP phases involving long organic spacers were reported in this class. Here, we report an all-inorganic RP phase lead halide perovskite, Cs2PbI2Cl2 (1, I4/mmm space group; a = 5.6385(8) angstrom, c = 18.879(4) angstrom), synthesized by a solid-state method. The compound exhibits a band gap of E-g similar to 3.04 eV and photoconductivity. We find an anomalous band gap evolution in Cs2Pb1-xSnxI2Cl2 solid solutions. Our combined density functional theory and experimental study supports the thermodynamically stable nature of 1 as a unique ordered phase in the Cs2PbX4 (X = Cl, Br, I) system. The calculations suggest that 1 is a direct bandgap semiconductor with relatively small effective carrier mass along the in-plane direction, consistent with the experimentally observed in-plane UV-light photoresponse. We also demonstrate that 1 is promising for radiation detection capable of alpha-particle counting. Moreover, 1 shows markedly ambient and thermal stability.