We propose and demonstrate a terahertz (THz) oscilloscope for recording time information of an ultrashort electron beam. By injecting a laser-driven THz pulse with circular polarization into a dielectric tube, the electron beam is swept helically such that the time information is uniformly encoded into the angular distribution that allows one to characterize both the temporal profile and timing jitter of an electron beam. The dynamic range of the measurement in such a configuration is significantly increased compared to deflection with a linearly polarized THz pulse. With this THz oscilloscope, nearly 50-fold longitudinal compression of a relativistic electron beam to about 15 fs (rms) is directly visualized with its arrival time determined with 3 fs accuracy. This technique bridges the gap between streaking of photoelectrons with optical lasers and deflection of relativistic electron beams with radio-frequency deflectors, and should have wide applications in many ultrashort electron-beam-based facilities.