Allocation and management of agricultural water resources is an emerging concern due to diminishing water supplies and increasing water demands. To achieve economic, social, and environmental goals in a specific irrigation district, decisions should be made subject to the changing water supply and water demand—the two critical random parameters in agricultural water resources management. This paper presents the foundations of a systematic framework for agricultural water resources management, including determination of distribution functions, joint probability of water supply and water demand, optimal allocation of agricultural water resources, and evaluation of various schemes according to agricultural water resources carrying capacity. The maximum entropy method is used to estimate parameters of probability distributions of water supply and demand, which is the basic for the other parts of the framework. The entropy-weight-based TOPSIS method is applied to evaluate agricultural water resources allocation schemes, because it avoids the subjectivity of weight determination and reflects the dynamic changing trend of agricultural water resources carrying capacity. A case study using an irrigation district in Northeast China is used to demonstrate the feasibility and applicability of the framework. It is found that the framework works effectively to balance multiple objectives and provides alternative schemes, considering the combinatorial variety of water supply and water demand, which are conducive to agricultural water resources planning.