IEEEThe spoof Surface Plasmon Polariton (sSPP) waveguides (WGs) are single conductor structures, which have a great potential for the demonstration of the novel and compact terahertz integrated systems. In this paper, we present a circuit model for the sSPP WGs, where all the reactive circuit model elements are calculated analytically, which is demonstrated for the first-time at the terahertz band. We also employ a modified version of the proposed model to a transition circuit, which enables the integration of the sSPP WGs with the conventional coplanar waveguides. In order to verify the proposed model experimentally, sSPP WGs with different physical dimensions have been designed, fabricated, and measured for 0.25-0.3 THz band. The measurements of the fabricated sSPP WGs show that the proposed model has an average and maximum phase errors of 2.2, 1.1, and 1.6% and 3.8, 1.7, and 1.9% at 0.25, 0.275, and 0.3 THz, respectively. The proposed model will enable the time-efficient design of the sSPP WGs together with the terahertz integrated circuits in the computer-aided design (CAD) environments.