Low seasonal precipitation and high demand for water use for agriculture, mining, industry, power generation and human consumption have made water resources management a concern in the Arequipa Region of Peru, which may be worse under future climate projections. In this study, the hydrologic response to climate change is evaluated within the Quilca-Vitor-Chili River Basin in the Arequipa Region of Peru. The Soil and Water Assessment Tool (SWAT) is used to develop a watershed model based on topographical, land cover, soil, and climatic (precipitation and temperature) data, while taking into account anthropogenic inter-basin transfers. The model is calibrated and validated for current conditions. Three climate scenarios derived from Atmosphere-Ocean General Circulation Model (AOGCM) simulations for both Representative Concentration Pathways (RCPs) 4.5 and 8.5 are obtained from the NASA Earth Exchange Global Daily Downscaled Projections (NEX-GDDP) dataset. Surface runoff and water yield associated with future climate scenarios are calculated for two near (2010-2039) and far (2040-2069) futures. Results of this study will provide a guideline for developing water policy in the region in order to mitigate negative impacts of climate variations in the region.