The Tarim River Basin (TRB) is one of the world’s largest cotton-producing areas, and its agricultural water use accounts for up to 95% of the total water consumption in the basin. Quantifying the future changes in the irrigation area carrying capacity under global warming is therefore essential in TRB. In this study, we analyzed the variation in the irrigation area in TRB over the last few decades, utilized the nonlinear autoregressive with an exogenous input neural network to simulate the future changes in the available water resources, and predicted the future irrigation area carrying capacity based on the water balance equation. The results showed that the present (1970–2020) irrigation area in TRB exhibited an increasing trend from 491 km2 in 1970s to 1382 km2 in 2020, as most of the natural vegetation was transformed into cropland. In the future (2022–2050), the available water resource will show an upward tendency while the irrigation area carrying capacity mainly ranges from 12×102–21×102 km2 and 17×102–30×102 km2 under scenarios SSP (shared socioeconomic pathway) 245 and SSP585, respectively. The simulated results will provide useful information for the allocation of water resources and the regional sustainable development of TRB.