The rapid decline in groundwater around the world poses a significant challenge to sustainable agriculture. To address this issue, agricultural managed aquifer recharge (Ag-MAR) is proposed to recharge the aquifer by artificially flooding agricultural lands using surface water. Ag-MAR requires a carefully selected flooding schedule to avoid affecting the oxygen absorption of crop roots. However, current Ag-MAR scheduling does not take into account complex environmental factors such as weather and soil oxygen, resulting in crop damage and insufficient recharging amounts. This paper proposes MARLP, the first end-to-end data-driven control system for Ag-MAR. We first formulate Ag-MAR as an optimization problem. To that end, we analyze four-year in-field datasets, which reveal the multi-periodicity feature of the soil oxygen level trends and the opportunity to use external weather forecasts and flooding proposals as exogenous clues for soil oxygen prediction. Then, we design a two-stage forecasting framework. In the first stage, it extracts both the cross-variate dependency and the periodic patterns from historical data to conduct preliminary forecasting. In the second stage, it uses weather-soil and flooding-soil causality to facilitate an accurate prediction of soil oxygen levels. Finally, we conduct model predictive control (MPC) for Ag-MAR flooding. To address the challenge of large action spaces, we devise a heuristic planning module to reduce the number of flooding proposals to enable the search for optimal solutions. Real-world experiments show that MARLP reduces the oxygen deficit ratio by 86.8% while improving the recharging amount in unit time by 35.8%, compared with the previous four years.