Parkinson's disease (PD) occupies the second position among neurodegenerative disorders in terms of global prevalence, its defining characteristic being a significant deficiency of dopamine in the central nervous system. Consequently, diagnosing PD poses significant challenges, often involving a lengthy process. This has driven extensive research efforts to identify reliable biomarkers for PD. One approach to identifying PD involves analyzing the characteristics of EEG signals. EEG records brain activity by measuring electrical signals from electrodes placed on the scalp. The emergence of Artificial Intelligence (AI) has enabled the integration of EEG signal features into machine learning (ML) algorithms, facilitating automated diagnosis of neurological diseases. These findings suggest that EEG signals hold significant potential as biomarkers for distinguishing between individuals with PD and healthy controls. This research explores the feasibility of using features extracted from EEG signals through Recurrence Quantification Analysis (RQA) as potential biomarkers for Parkinson's Disease (PD). Utilizing publicly available EEG data from The Patient Repository for EEG Data + Computational Tools (PRED + CT), we analyzed recordings from PD patients who underwent repeated auditory stimulation tests. Different machine learning models, including Support Vector Machine (SVM), K-Nearest Neighbors (KNN), Decision Tree (DT), Random Forest (RF), Gentle Boosting (GentleBoost), Quadratic Discriminant Analysis (QDA), and Multilayer Perceptron (MLP), were used in both multiclass and binary classification scenarios. The performance of the aforementioned models was evaluated using a 10-fold cross-validation method. The proposed method achieved an average accuracy of 99.32% in the binary classification scenario (distinguishing between Parkinson's disease patients and healthy individuals) and an average accuracy of 98.30% in the multiclass classification using the KNN classifier. The results suggest that the RQA-based features extracted from electroencephalographic signals show promising potential as biomarkers for Parkinson's disease.