Using daily data from January 3, 2001 to July 17, 2020 we analyze the impact of oil market uncertainty (computed based on the realized volatility of five-minute intraday oil returns) on the level, slope and curvature factors derived from the term structure of US interest rates covering maturities from 1 to 30 years. The results of the linear Granger causality tests show no evidence of the predictive ability of oil uncertainty for the three latent factors. However, evidence of nonlinearity and structural breaks indicates misspecification of the linear model. Accordingly, we use a data-driven approach: the nonparametric causality-in-quantiles test, which is robust to misspecification due to nonlinearity and regime change. Notably, this test allows us to model the entire conditional distribution of the level, slope and curvature factors, and hence accommodate, via the lower quantiles, the zero lower bound situation observed in our sample period. Using this robust test, we find overwhelming evidence of causality from oil uncertainty for the entire conditional distribution of the three factors, suggesting the predictability of the entire US term structure based on information contained in oil market volatility. Our results have important implications for academics, investors and policy makers.