Orthotropic steel bridge deck rib-to-deck (RD) joints are susceptible to fatigue cracking under coupled vehicle and temperature loading. To address the high computational cost of finite element analysis and the lack of physical constraints in purely data-driven models, this study proposes a data–physics dual-driven fatigue life prediction model based on a Physics-Informed Temporal Convolutional Network (PI-TCN). An RD-joint local model containing a semi-elliptical surface crack is established using ABAQUS–FRANC3D co-simulation and the submodeling technique to simulate crack propagation under coupled vehicle–temperature loading. A fatigue life dataset incorporating crack dimensions, equivalent load, temperature, and coupled stress ratio is subsequently constructed. The model employs dilated causal convolutions to extract temporal features and combines the Paris-law residual with the supervised loss to form a joint loss function, thereby constraining the monotonicity and physical consistency of crack propagation. The results show that PI-TCN achieves lower prediction errors than the purely data-driven TCN model and can mitigate non-physical fluctuations, such as decreases in crack depth. In independent tests, the model successfully tracks fatigue lives ranging from 0.5 to 2.5 million cycles. The absolute errors of most samples are within 100,000 cycles, and the mean absolute percentage error of representative samples is approximately 2.85%. The proposed method improves the accuracy and stability of fatigue life prediction for RD joints.