Drug repositioning is a cost-effective strategy that seeks new therapeutic uses for existing drugs and fundamentally depends on identifying potential drug-disease associations. Drug repositioning entails inherent complexity: one must model not only cross-type relationships (drug-disease) but also intra-type relationships (drug-drug and disease-disease), while accounting for the modulatory effects of auxiliary biomedical entities (e.g., targets, pathways). However, existing methods overlook the discrepancy in information granularity among multi-level relationships. To address this problem, we propose AURORA, an adaptive multi-granularity graph learning framework with consistency regularization for drug repositioning. Specifically, AURORA integrates fine-grained representations from a biomedical heterogeneous graph and coarse-grained features derived from drug and disease hypergraphs. Then, AURORA employs a bidirectional attention mechanism to adaptively fuse representations from different granularity graphs, while a consistency regularization term aligns embeddings across granularities. Finally, the optimized drug and disease embeddings are fed into a gradient boosting predictor to produce drug-disease association likelihood scores. Extensive experiments demonstrate that AURORA outperforms state-of-the-art methods in predicting unknown drug-disease associations. Additionally, we conduct case studies to show the capability of AURORA to predict candidate drugs for complex diseases. The source code is available at https://github.com/ZhangYid/AURORA.