The aim of this study is to propose a practical smartphone-based tool to accurately assess upper limb tremor in Parkinson's disease (PD) patients. The tool uses signals from the phone's accelerometer and gyroscope (as the phone is held or mounted on a subject's hand) to compute a set of metrics which can be used to quantify a patient's tremor symptoms. In a small-scale clinical study with 25 PD patients and 20 age-matched healthy volunteers, we combined our metrics with machine learning techniques to correctly classify 82% of the patients and 90% of the healthy volunteers, which is high compared to similar studies. The proposed method could be effective in assisting physicians in the clinic, or to remotely evaluate the patient's condition and communicate the results to the physician. Our tool is low cost, platform independent, noninvasive, and requires no expertise to use. It is also well matched to the standard clinical examination for PD and can keep the patient "connected" to his physician on a daily basis. Finally, it can facilitate the creation of anonymous profiles for PD patients, aiding further research on the effectiveness of medication or other overlooked aspects of patients' lives.