Scour is a natural process that involves the removal of bed material by the action of flowing water, which eventually removes sediment around or near the river structure such as bridge pier and exposes its foundation located in a flowing stream. Excessive scour may result in the failure of the foundation and collapse of the structure; therefore, predicting the maximum scour depth is an important aspect of bridge pier design. This study uses the HEC-RAS Version 6.3.1 software to estimate the bridge scour of the Orsang Aqueduct built over the Orsang River. A one-dimensional hydraulic model of Orsang River reach using HEC-RAS is constructed for predicting flow parameters. With a design flood of 12,063 cumecs, flow conditions were simulated, and maximum scour depths were predicted. The scour depths are also calculated for flood magnitudes, i.e., 25, 50, 75, 107, 120, and 136% of the design flood. A sensitivity study is carried out for different Manning’s values and different angles of attack on the pier. Orsang River is a source of good quality sand with varying depths about 10–25 m to meet the construction demand of nearby areas. The riverbed degradation is observed due to sand extraction to a large extent. The scour depth is also predicted if the river bed is further degraded by 0.5, 1, or 2 m with the river under design flood. The predicted scour depth values are compared with different empirical equations for local scour. The total scour depth predicted is also compared with the result of model studies performed by GERI (Gujarat Engineering Research Institution). The HEC-RAS model appears to produce more realistic results since it incorporates more relevant elements such as angle of attack, bed conditions, piers shape, flow concentrations, flow depth, and Froude Number. Estimating scour depth helps to recommend appropriate scour protection measures to protect the structure.