With nearly two billion stars observed and their corresponding astrometric parameters evaluated in the recent Gaia mission, the number of astrometric binary candidates have risen significantly. Due to the surplus of astrometric data, the current computational methods employed to inspect these astrometric binary candidates are both computationally expensive and cannot be executed in a reasonable time frame. In light of this, a machine learning (ML) technique to automatically classify whether a set of stars belong to an astrometric binary pair via an artificial neural network (ANN) is proposed. Using data from Gaia DR3, the ANN was trained and tested on 1.5 million highly probable true and visual binaries, considering the proper motions, parallaxes, and angular and physical separations as features. The ANN achieves high classification scores, with an accuracy of 99.3%, a precision rate of 0.988, a recall rate of 0.991, and an AUC of 0.999, indicating that the utilized ML technique is a highly effective method for classifying astrometric binaries. Thus, the proposed ANN is a promising alternative to the existing methods for the classification of astrometric binaries.