We present a robust practical scheme for measuring the topological invariants of non-interacting tight-binding models realized in arrays of coupled photonic cavities. More specifically, we aim to focus on the implementation of a single unit cell with tunable twisted boundary conditions in order to access the bulk topological properties of much larger systems experimentally. We illustrate our method in a two-dimensional integer quantum Hall model, demonstrating that the associated topological invariants can be measured to a high degree of accuracy despite the driven-dissipative bosonic nature of the system, and discuss the robustness of our scheme against various sources of disorder.