Large-scale whole-genome sequencing studies have enabled the analysis of rare variants (RVs) associated with complex phenotypes. Commonly used RV association tests have limited scope to leverage variant functions. We propose STAAR (variant-set test for association using annotation information), a scalable and powerful RV association test method that effectively incorporates both variant categories and multiple complementary annotations using a dynamic weighting scheme. For the latter, we introduce 'annotation principal components', multidimensional summaries of in silico variant annotations. STAAR accounts for population structure and relatedness and is scalable for analyzing very large cohort and biobank whole-genome sequencing studies of continuous and dichotomous traits. We applied STAAR to identify RVs associated with four lipid traits in 12,316 discovery and 17,822 replication samples from the Trans-Omics for Precision Medicine Program. We discovered and replicated new RV associations, including disruptive missense RVs of NPC1L1 and an intergenic region near APOC1P1 associated with low-density lipoprotein cholesterol.