Delirium is an acute brain disorder that commonly occurs in patients with acute ischemic stroke (AIS). Pathomechanism of delirium is related to the neuroinflammatory process and oxidative stress. Search for readily available diagnostic marker that will aid clinicians in early identification of delirium is ongoing. The aim of this study was to investigate whether neutrophil-to-lymphocyte ratio (NLR) could serve as a potential marker for delirium prediction in patients with AIS and to find an easy diagnostic tool using laboratory and clinical parameters to predict delirium. Prospective observational study (NCT03944694) included patients with AIS admitted to the neurology department of a district general hospital. All patients were screened for delirium using CAM-ICU (Confusion Assessment Method for Intensive Care Unit). Demographic and medical history data and admission lab results, including differential white blood cell analysis, were collected from all patients. We included 1001 patients in the final analysis. The mean age of the sample was 71 years, and 52% of patients were males. The incidence of early-onset delirium was 17.2%. The NLR was elevated in delirious patients (6.39 ± 8.60 vs. 4.61 ± 5.61, p < 0.001). The best cut-off value of NLR to predict delirium using the receiver operating characteristics (ROC) was determined at 4.86. Multivariable logistic regression analysis showed that the odds ratio (OR) for developing delirium with NLR > 4.86 (adjusted for age, sex, body mass index (BMI), comorbidities, and baseline neurology) was 1.875 (95% CI 1.314–2.675, p = 0.001). As a result of different combinations of markers and clinical parameters based on logistic regression, a formula—DELirium in Acute Ischemic Stroke (DELIAS score)—was obtained with the area under the ROC curve of 0.801 (p < 0.001). After regression of the cut-off points of the obtained curve, a significant correlation of the DELIAS score was observed with the occurrence of early-onset delirium (OR = 8.976, p < 0.001) and with delirium until the fifth day after AIS (OR = 7.744, p < 0.001). In conclusion, NLR can be regarded as a potential marker for prediction of early-onset delirium after AIS. On the basis of combined laboratory and clinical parameters, the DELIAS score was calculated, which gave the highest predictive value for delirium in the analyzed group of patients after ischemic stroke. However, further studies are needed to validate these findings.