We report on the experimental observation of the topological Anderson phase in one-dimensional quasi-periodical waveguide arrays produced by femtosecond laser writing. The evanescently coupled waveguides are with alternating coupling constants, constructing photonic lattices analogous to the Su-Schrieffer-Heeger model. Dynamic tuning of the interdimer hopping amplitudes of the waveguide array generates the quasi-periodic disorder of the coupling constants for the model. As light propagates in the corresponding photonic waveguides, it exhibits different modes depending on the magnitude of the disorder. The topological Anderson phase is observed as the disorder is sufficiently strong, which corresponds to the zero-energy mode in its spectrum. The experimental results are consistent with the theoretical simulations, confirming the existence of the disorder-driven topological phase from a trivial band in the photonic lattice.