Connected speech elicited by picture-description tasks offers a sensitive, non-invasive window into psychopathology and is increasingly relevant for digital health applications. In psychotic disorders, narrative disorganization and prosodic abnormalities have been linked to illness severity and functional outcome. This study examined whether acoustic speech markers can serve as objective, scalable biomarkers of psychosis. We enrolled 28 adults (18–65 years) with DSM-5 psychotic disorders (PD) and 15 healthy controls (HC) who completed the Boston Diagnostic Aphasia Examination “Cookie Theft” picture description. Major neurological disease, aphasia, intellectual disability, acute substance intoxication, and comorbid major depressive disorder were exclusion criteria. Acoustic features included mean and variability of pitch, spectral centroid and bandwidth, root mean square (RMS) energy, Mel-frequency cepstral coefficients (MFCCs), and gammatone filterbank metrics. Three machine learning (ML) approaches have been applied to classify PD and HC, namely support vector machine (SVM), Logistic regression, and decision tree. The SVM classifier achieved the best performance reaching an area under the curve of the receiver operating curve (ROC-AUC) of 0.95. If replicated in larger samples, this approach may function as a practical digital biomarker to complement clinical scales for early detection, individualized prognosis, and longitudinal treatment monitoring.