This paper proposes a novel structure to optimize the operational strategies of responsive farms for day-ahead peak shaving. To achieve the aim, the modern irrigation system of farms, including groundwater, surface water, and booster water pumps, are modeled mathematically. To develop the demand response (DR) potentials of the farms, electrical storage systems, and self-generation facilities, including thermal distributed generations and on-farm solar sites, are addressed. In order to facilitate the integration of the agricultural DR programs into the electricity market, a mathematical formulation for agricultural demand response aggregator (ADRA) is suggested. The ADRA participates in the day-ahead electricity market on behalf of the responsive farms. To overcome the price uncertainty of the electricity market, a robust optimization approach is addressed. This approach determines the robust decisions of farms in the worst-case realizations of the uncertain electricity price. Regarding on-farm solar sites located in rural areas, a data-driven approach is used to estimate the solar power generation of a significant number of sites without needing to install costly communication and measurement infrastructures. Finally, the proposed approach is implemented on agricultural lands in the northeast of Iran. The numerical results show that the suggested approach provides day-ahead peak shaving for the power systems meeting the crop's water requirements.