Climate change has significantly influenced water resource patterns in arid regions. Applying effective water-saving measures to improve irrigation efficiency and evaluate their future water-saving capabilities is crucial for ensuring the sustainable development of irrigation agriculture. Based on the daily meteorological data from 15 global climate models (GCMs) in the sixth phase of the Coupled Model Intercomparison Project (CMIP6), this study used the AquaCrop model to perform high-resolution (0.1° × 0.1°) grid simulations of cotton yields and irrigation requirements. The study also investigated the ability of film-mulched drip irrigation (FMDI) to improve future irrigation efficiency under two shared socio-economic pathways (SSP245 and SSP585) in the Tarim River Basin (TRB), Central Asia, from 2025 to 2100. The results showed that the cotton yield and irrigation water productivity (WPI) in the TRB exhibited an upward trend of 13.82 kg/ha/decade (80.68 kg/ha/decade) and 0.015 kg/m3/decade (0.068 kg/m3/decade), respectively, during the study period. The cotton yield and WPI were higher in the northern, northwestern plains, and northeastern intermountain basin areas, where they reach over 4000 kg/ha and 0.8 kg/m3/decade. However, the cotton yield and WPI were lower in the southwestern part of the study area. Therefore, large-scale cotton production was not recommended there. Furthermore, compared to flood irrigation, the use of FMDI can, on average, improve the WPI by approx. 25% and reduce irrigation water requirements by more than 550 m3/ha. Therefore, using FMDI can save a substantial amount of irrigation water in cotton production, which is beneficial for improving irrigation efficiency and ensuring the future stable production of cotton in the TRB. The research results provide a scientific reference for the efficient utilization and management of water resources for cotton production in the TRB and in similar arid regions elsewhere in the world.