Dense genotype data and thousands of phenotypes from large biobanks, coupled with increasingly accessible summary association statistics from genome-wide association studies (GWAS), provide great opportunities to dissect the complex relationships among human traits and diseases. We introduce BADGERS, a powerful method to perform polygenic score-based biobank-wide scans for disease-trait associations. Compared to traditional regression approaches, BADGERS uses GWAS summary statistics as input and does not require multiple traits to be measured on the same cohort. We applied BADGERS to two independent datasets for Alzheimer's disease (AD; N=61,212). Among the polygenic risk scores (PRS) for 1,738 traits in the UK Biobank, we identified 48 significant trait PRSs associated with AD after adjusting for multiple testing. Family history, high cholesterol, and numerous traits related to intelligence and education showed strong and independent associations with AD. Further, we identified 41 significant PRSs associated with AD endophenotypes. While family history and high cholesterol were strongly associated with neuropathologies and cognitively-defined AD subgroups, only intelligence and education-related traits predicted pre-clinical cognitive phenotypes. These results provide novel insights into the distinct biological processes underlying various risk factors for AD.