In this work, we report on the implementation of a time-domain integrator device operating on arbitrary broadband Terahertz (THz) pulses. This analog signal-processing functionality is implemented by employing a two-wire waveguide (TWWG) variant, based on a tapered configuration. A conventional TWWG is made of two copper wires separated by an air gap between them. Here, we show here that, if the gap between the wires is much smaller than the THz wavelength and the wire radius, the propagating THz field undergoes a field enhancement factor that is inversely proportional to the THz frequency, thus matching with the spectral behavior of a time-domain integrator. Both simulation and experimental results here demonstrate that the tapered TWWG (briefly, TTWWG) is indeed able to perform the time-domain integration functionality.