Subtomogram alignment is a critical task in cryo-electron tomography (cryo-ET) analysis, essential for achieving high-resolution reconstructions of macromolecular complexes. However, learning effective positional representations remains challenging due to limited labels and high noise levels inherent in cryo-ET data. In this work, we address this challenge by proposing a self-supervised learning approach that leverages intrinsic geometric transformations as implicit supervisory signals, enabling robust representation learning despite data scarcity. We introduce BOE-ViT, the first Vision Transformer (ViT) framework for 3D subtomogram alignment. Recognizing that traditional ViTs lack equivariance and are therefore suboptimal for orientation estimation, we enhance the model with two innovative modules that introduce equivariance include 1) the Polyshift module for improved shift estimation and 2) Multi-Axis Rotation Encoding (MARE) for enhanced rotation estimation. Experimental results demonstrate that BOE-ViT significantly outperforms state-of-the-art methods. Notably, at SNR 0.01 dataset, our approach achieves a 77.3\% reduction in rotation estimation error and a 62.5\% reduction in translation estimation error, effectively overcoming the challenges in cryo-ET subtomogram alignment.