Recent advancements have brought significant attention to photonic terahertz (THz)-integrated sensing and communication (ISAC) systems. In this work, we present an adaptive frequency offset (FO) compensation method for dual-chirp-based ISAC waveforms, using the fractional Fourier transform (FrFT) method. The proposed scheme can enable frequency synchronization without a need for training preambles and exhibit robustness against system noise. We validate this approach through an experimental demonstration in a 300 GHz photonic THz-ISAC system with 20 Gbps quadrature-phase shift keying (QPSK) data transmission and 1.5 cm range resolution. The experiment successfully compensates for frequency offsets ranging from −5 to 5 GHz, achieving an estimation error of less than 0.08% and a chirp-pilot power overhead of 0.5%.