This paper develops a simple and new approach for testing linear hypotheses about autocorrelations for time series with general stationary serial correlation structures. A practically important special case is the computation of robust confidence intervals for individual autocorrelations that do not require resampling methods. Inference is heteroskedasticity and autocorrelation robust (HAR) and allows innovations to be uncorrelated but not necessarily independent and identically distributed (iid). It is well known that the classic Bartlett (1946) formula can provide invalid inference when innovations are not (iid). Romano and Thombs (1996) derive the asymptotic distribution of sample autocorrelations under weak assumptions but avoid estimation of the variances of sample autocorrelations and suggest resampling schemes to obtain confidence intervals. As an alternative we provide an easy to implement regression approach for estimating autocorrelations and their variance matrices. The asymptotic variance takes a sandwich form which can be estimated using well known HAR variance estimators. Resulting test statistics can be implemented with fixed-smoothing critical values which reduce finite sample size distortions. Monte Carlo simulations show our approach is robust to innovations that are not iid and works reasonably well across various serial correlation structures. An empirical illustration using robust confidence intervals for autocorrelations of S&P 500 index returns shows that conclusions about market efficiency and volatility clustering during pre and post-Covid periods using our approach contrast with conclusions using traditional (and often incorrectly used) methods. We provide a Python implementation for practitioners that implements our approach: https://eastlansing.github.io/Robust_CI_Acf/