This study aimed to develop an artificial intelligence (AI)-based tool for screening COVID-19 patients based on the acoustic parameters of their voices. Twenty-five acoustic parameters were extracted from voice samples of 203 COVID-19 patients and 171 healthy individuals who produced a sustained vowel, i.e., /a/, as long as they could after a deep breath. The selected acoustic parameters were from different categories including fundamental frequency and its perturbation, harmonicity, vocal tract function, airflow sufficiency, and periodicity. After the feature extraction, different machine learning methods were tested. A leave-one-subject-out validation scheme was used to tune the hyper-parameters and record the test set results. Then the models were compared based on their accuracy, precision, recall, and F1-score. Based on accuracy (89.71%), recall (91.63%), and F1-score (90.62%), the best model was the feedforward neural network (FFNN). Its precision function (89.63%) was a bit lower than the logistic regression (90.17%). Based on these results and confusion matrices, the FFNN model was employed in the software. This screening tool could be practically used at home and public places to ensure the health of each individual's respiratory system. If there are any related abnormalities in the test taker's voice, the tool recommends that they seek a medical consultant.