Terahertz (THz) integrated sensing and communication (ISAC) is a promising interdisciplinary technology that realizes simultaneously transmitting Terabit-per-second (Tbps) and millimeter-level accurate environment or human activity sensing. However, both communication performance and sensing accuracy are influenced by the Doppler effects, which are especially severe in the THz band. Moreover, peak-to-average power ratio (PAPR) degrades the THz power amplifier (PA) efficiency. In this paper, a discrete Fourier transform spread orthogonal time frequency space (DFT-s-OTFS) system with superimposed pilots is proposed to improve the robustness to Doppler effects and reduce PAPR for THz ISAC. Then, a two-phase sensing parameter estimation algorithm is developed to integrate sensing functionality into the DFT-s-OTFS waveform. Meanwhile, a low-complexity iterative channel estimation and data detection method with a conjugate gradient based equalizer is proposed to recover the data symbols of DFT-s-OTFS. The proposed DFT-s-OTFS waveform can improve the PA efficiency by 10% on average compared to OTFS. Simulation results demonstrate that the proposed two-phase sensing estimation algorithm for THz DFT-s-OTFS systems is able to realize millimeter-level range estimation accuracy and decimeter-per-second-level velocity estimation accuracy. Moreover, the effectiveness of the iterative method for data detection aided by superimposed pilots in DFT-s-OTFS systems is validated by the simulations and the bit error rate performance is not degraded by the Doppler effects.