The increasing availability of whole-genome sequencing (WGS) has begun to elucidate the contribution of rare variants (RVs), both coding and non-coding, to complex disease. Multiple RV association tests are available to study the relationship between genotype and phenotype, but most are restricted to per-gene models and do not fully leverage the availability of variant-level functional annotations. We propose Genome-wide Rare Variant EnRichment Evaluation (gruyere), a Bayesian probabilistic model that complements existing methods by learning global, trait-specific weights for functional annotations to improve variant prioritization. We apply gruyere to WGS data from the Alzheimer's Disease (AD) Sequencing Project, consisting of 7,966 cases and 13,412 controls, to identify AD-associated genes and annotations. Growing evidence suggests that disruption of microglial regulation is a key contributor to AD risk, yet existing methods have not had sufficient power to examine rare non-coding effects that incorporate such cell-type specific information. To address this gap, we 1) use predicted enhancer and promoter regions in microglia and other potentially relevant cell types (oligodendrocytes, astrocytes, and neurons) to define per-gene non-coding RV test sets and 2) include cell-type specific variant effect predictions (VEPs) as functional annotations. gruyere identifies 15 significant genetic associations not detected by other RV methods and finds deep learning-based VEPs for splicing, transcription factor binding, and chromatin state are highly predictive of functional non-coding RVs. Our study establishes a novel and robust framework incorporating functional annotations, coding RVs, and cell-type associated non-coding RVs, to perform genome-wide association tests, uncovering AD-relevant genes and annotations.