Augmented reality (AR) applications for construction monitoring rely on real-time environmental tracking to visualize architectural elements. However, construction sites present significant challenges for traditional tracking methods due to featureless surfaces, dynamic changes, and drift accumulation, leading to misalignment between digital models and the physical world. This paper proposes a BIM-aware drift correction method to address these challenges. Instead of relying solely on SLAM-based localization, we align ``as-built" detected planes from the real-world environment with ``as-planned" architectural planes in BIM. Our method performs robust plane matching and computes a transformation (TF) between SLAM (S) and BIM (B) origin frames using optimization techniques, minimizing drift over time. By incorporating BIM as prior structural knowledge, we can achieve improved long-term localization and enhanced AR visualization accuracy in noisy construction environments. The method is evaluated through real-world experiments, showing significant reductions in drift-induced errors and optimized alignment consistency. On average, our system achieves a reduction of 52.24% in angular deviations and a reduction of 60.8% in the distance error of the matched walls compared to the initial manual alignment by the user.