Parkinson's disease currently affects millions of people worldwide and is steadily increasing. Many symptoms are associated with this disease, including rest tremor, bradykinesia, stiffness or rigidity of the extremities and postural instability. No cure is currently available for Parkinson's disease patients; instead most medications are for treatment of symptoms. This treatment depends on the quantification of these symptoms such as hand tremor. This work proposes a new system for mobile phone applications. The system is based on measuring the acceleration from the Parkinson's disease patient's hand using a mobile cell phone accelerometer. Recordings from 21 Parkinson's disease patients and 21 healthy subjects were used. These recordings were analysed using a two level wavelet packet analysis and features were extracted forming a feature vector of 12 elements. The features extracted from the 42 subjects were classified using a neural networks classifier. The results obtained showed an accuracy of 95% and a Kappa coefficient of 90%. These results indicate that a cell phone accelerometer can accurately detect and record rest tremor in Parkinson's disease patients.