This work presents the optical fiber (OF) sensor for arterial pulse waveform (APW) measurement, the operation of which is based on the method of applanation tonometry. The measured optical signal, which is used to determine the APW at different arterial pulse points is created in the sensor by reflection from two reflective surfaces. The first reflective surface is the front-end surface of the OF, and the second reflective surface is the surface of the flexible membrane that is attached to the arterial pulse point. The reflective surfaces of the sensor create a low-finesse Fabry-Perot cavity from which the optical interference signal is measured in the time domain. In this article, we show that by analyzing the phase of the interference signal in the time domain, it is possible to reconstruct the APW with high accuracy. Concurrently, we document that in interference signals, there are well-identifiable places that determine the start of systole, peak systole, dicrotic notch, and end of diastole. We describe the detailed construction of the prepared sensor and the method of its use, and we demonstrate using of the sensor in measuring the APW on the carotid, femoral, radial, and posterior tibial arteries.