Indirect absorption extended below the direct transition edge and increase in carrier lifetime derived from Rashba spin-orbit coupling may advance the optoelectronic applications of metal halide perovskites. Spin-orbit coupling in halide perovskites is due to the presence of heavy elements in their structure. However, when these materials lack an inversion symmetry, for example by the application of strain, spin-orbit coupling becomes odd in the electron's momentum giving rise to a splitting in the electronic energy bands. Here we report on the observation of a large Rashba splitting of 117 meV at room temperature, as predicted by relativistic first-principles calculations, in halide perovskite single crystals through a facile compositional engineering approach. Partial substitution of organic cations by rubidium in single crystals induces significant indirect absorption and dual peak photoluminescence as a result of a large Rashba splitting. We measured circularly polarized photoluminescence and magneto-photoluminescence in perovskite films printed by single crystals as well as magnetoelectroluminescence and magneto-photocurrent in spin-LEDs based on perovskite single crystals. They indicated significant spin-momentum locking due to the large Rashba effect. A hybrid perovskite single crystal photodetector achieved record figures of merit, including detectivity of more than 1.3 x 10(18) Jones which represents a three orders of magnitude improvement compared to the to date record. These findings show that facile compositional engineering of perovskite single crystals holds great promise for further advancing the optoelectronic properties of existing materials.