We present the analysis and design of fixed physical length, spoof Surface Plasmon Polariton based waveguides with adjustable delay at terahertz frequencies. The adjustable delay is obtained using Corrugated Planar Goubau Lines (CPGL) by changing its corrugation depth without changing the total physical length of the waveguide. Our simulation results show that electrical lengths of 237.9°, 220.6°, and 310.6° can be achieved by physical lengths of 250 μm and 200 μm at 0.25, 0.275, and 0.3 THz, respectively, for demonstration purposes. These simulations results are also consistent with our analytical calculations using the physical parameter and material properties. When we combine pairs of same length delay lines as if they are two branches of a terahertz phase shifter, we achieved an error rate of relative phase shift estimation better than 5.8%. To the best of our knowledge, this is the first-time demonstration of adjustable spoof Surface Plasmon Polariton based CPGL delay lines. The idea can be used for obtaining tunable delay lines with fixed lengths and phase shifters for the terahertz band circuitry.