Terahertz- (THz-) based electron manipulation has recently been shown to hold tremendous promise as a technology for manipulating and driving the next generation of compact ultrafast electron sources. Here, we demonstrate an ultrafast electron diffractometer with THz-driven pulse compression. The electron bunches from a conventional DC gun are compressed by a factor of 10 and reach a duration of ~180 fs (FWHM) with 10,000 electrons/pulse at a 1 kHz repetition rate. The resulting ultrafast electron source is used in a proof-of-principle experiment to probe the photoinduced dynamics of single-crystal silicon. The THz-compressed electron beams produce high-quality diffraction patterns and enable the observation of the ultrafast structural dynamics with improved time resolution. These results validate the maturity of THz-driven ultrafast electron sources for use in precision applications.