Direct current (DC) arcs frequently occur in DC power systems, and accurate modeling of their behavior is essential for enhancing system safety and reliability. Traditional arc models often suffer from a trade-off between computational efficiency and physical accuracy, limiting their effectiveness in circuit-level simulation. To overcome this challenge, we propose a black-box DC arc model that couples a 1D arc decaying model with a deep operator network (DeepONet). Compared with conventional models, the proposed approach achieves significantly higher computational efficiency and lower prediction error under typical operating conditions. In addition, we develop a DeepONet-based parameter identification method that enables robust calibration of key arc parameters (e.g., arc radius and length), ensuring both accuracy and physical interpretability. The model and identification method are validated through experiments on arc cases with currents of 40, 60, and 80 A. Results demonstrate that the proposed model supports efficient, circuit-level simulations while retaining physical meaning and real-time computational performance, offering a novel approach to DC arc modeling.