We report the first experimental demonstration of linear electron acceleration using an optically generated single-cycle THz pulse centered at 0.45 THz. 7 keV of acceleration is achieved using 10 μJ THz pulses in a 3 mm interaction length. The THz pulse is produced via optical rectification of a 1.2 mJ, 1 μm laser pulse with a 1 kHz repetition rate. The THz pulse is coupled into a dielectric-loaded circular waveguide with 10 MeV/m on-axis accelerating gradient. A 25 fC input electron bunch is produced with a 60 keV DC photo-emitting cathode. The achievable accelerating gradient in the THz structures being investigated will scale rapidly by increasing the IR pulse energy (100 mJ - 1 J) and correspondingly the THz pulse energy. Additionally, with recent advances in the generation of THz pulses via optical rectification, in particular improvements to efficiency and generation of multi-cycle pulses, GeV/m accelerating gradients could be achieved. An ultra-compact high-gradient THz accelerator would be of interest for a wide variety of applications.