Alcohol use disorder (AUD) is a major component in the etiology of cognitive decline and dementia. Underlying mechanisms by which long-term alcohol abuse causes cognitive dysfunction include excessive oxidative stress and inflammation in the brain, activated by increased reactive oxygen/nitrogen species (ROS/RNS), advanced glycation end-products (AGEs) and high-mobility group box 1 protein (HMGB1). In a pilot study, we examine the potential clinical value of circulating biomarkers of oxidative stress including ROS/RNS, HMGB1, the soluble receptor for AGE (sRAGE), the brain biomarker of aging apolipoprotein D (ApoD), and the antioxidant regulator nuclear factor erythroid 2-related factor 2 (NRF2) as predictive indices for cognitive impairment (CI) in abstinent patients with AUD (n = 25) compared to patients with established Alzheimer’s disease (AD, n = 26) and control subjects (n = 25). Plasma concentrations of sRAGE were evaluated with immunoblotting; ROS/RNS with a fluorometric kit; and HMGB1, ApoD, and NRF2 by ELISA. Abstinent AUD patients had higher sRAGE, ROS/RNS (p < 0.05), and ApoD (p < 0.01) concentrations, similar to those of AD patients, and lower NRF2 (p < 0.01) concentrations, compared to controls. These changes were remarkable in AUD patients with CI. HMGB1, and sRAGE correlated positively with duration of alcohol use (rho = 0.398, p = 0.022; rho = 0.404, p = 0.018), whereas sRAGE correlated negatively with periods of alcohol abstinence (rho = −0.340, p = 0.045). A predictive model including ROS/RNS, HMGB1, sRAGE, alcohol use duration, and alcohol abstinence periods was able to differentiate AUD patients with CI (92.3% of correct predictions, ROC-AUC= 0.90) from those without CI. In conclusion, we propose ROS/RNS, HMGB1, and sRAGE as stress biomarkers capable of predicting cognitive impairment in AUD patients.