Pulse shaping is important for communications, spectroscopy, and other applications that require high peak power and pulsed operation, such as radar systems. Unfortunately, pulse shaping remains largely elusive for terahertz (THz) frequencies. To address this void, a comprehensive study on the dispersion tunability properties of THz chirped pulses traveling through a dielectric-lined hollow-core waveguide loaded with a helical graphene ribbon is presented. It is demonstrated that there is an optimal compression waveguide length over which THz chirped pulses reach the maximum compression. The optimal length is dependent on the chirp pulse duration. It is shown that by applying an electrostatic controlling gate voltage (Vg) of 0 and 30 V on the helical graphene ribbon, the temporal input pulses of width 8 and 12 ps, propagating through two different lengths, can be tuned by 5.9% and 8%, respectively, in the frequency range of 2.15-2.28 THz.