Photoinduced spin-charge interconversion in semiconductors with spin-orbit coupling could provide a route to optically addressable spintronics without the use of external magnetic fields. However, in structurally disordered polycrystalline semiconductors, which are being widely explored for device applications, the presence and role of spin-associated charge currents remains unclear. Here, using femtosecond circular-polarization-resolved pump-probe microscopy on polycrystalline halide perovskite thin films, we observe the photoinduced ultrafast formation of spin domains on the micrometre scale formed through lateral spin currents. Micrometre-scale variations in the intensity of optical second-harmonic generation and vertical piezoresponse suggest that the spin-domain formation is driven by the presence of strong local inversion symmetry breaking via structural disorder. We propose that this leads to spatially varying Rashba-like spin textures that drive spin-momentum-locked currents, leading to local spin accumulation. Ultrafast spin-domain formation in polycrystalline halide perovskite films provides an optically addressable platform for nanoscale spin-device physics.