Multi-view subspace clustering optimizes accuracy through the integration of intrinsic data from diverse views. However, current methods, despite their strong clustering performance, grapple with scalability due to high time complexity. The potential of anchor-based models to address this challenge is noteworthy, yet they often disregard higher-order relationships and crucial complementary insights that exist among views. To tackle these issues, we present a Tensorized Structural Anchor-based Method for Scalable Multi-view Subspace Clustering (TSA-SMSC). Firstly, TSA-SMSC characterizes the high-order collections by minimizing the tensor regularization on the third-order tensor, which comprises anchor graph matrices from different views. More importantly, we propose a novel self-weighted tensor logarithmic Schatten-p function, which enables us to effectively capture structural complementarity by incorporating the distinctions between singular values using adaptive weights. Finally, we design a structural fusion term to constrain connected components in anchor graphs and facilitate consensus representation. Extensive experiments on six large-scale datasets demonstrate the superiority of our proposed framework.