Cerebellar Ataxia (CA) is a neurological condition that leads to uncoordinated muscle movements, even affecting the production of speech. Effective biomarkers are necessary to produce an objective decision-making support tool for early diagnosis of CA in non-clinical environments. This paper investigates the reliability and effectiveness of vocal tract acoustic biomarkers for assessing CA speech. These features were tested on a database consisting of 52 clinically rated tongue-twister phrase 'British Constitution' and its 4 consonant-vowel (CV) excerpts /ti/, /ti/', /tu/, /tion/ acquired from 30 ataxic patients and 22 healthy controls. Such a marker could be applied to objectively assess the severity of CA from a simple speaking test, contributing to the possibility of being translated into a computer based automatic module to screen the disease from the speech. All the vocal tract features explored in this study were statistically significant using Kolmogorov-Smirnov test at 5% level in distinguishing healthy and CA speech. Several machine learning classifiers with 5-fold cross-validations were implemented on the vocal features. It was observed that the intensity ratios corresponding to the 4 C-V excerpts in CA group showed an increased variability and produced the best classification accuracy of 84.6% using KNN classifier. Results motivate the use of vocal tract features for monitoring CA speech.