A programmable topological photonic chip is introduced, enabling precise control of light's topological phases through silicon photonic nanocircuits and microresonators. The chip allows individual programming of artificial atoms and their interactions, enabling dynamic topological phase transitions and diverse photonic topological insulators. It can be rapidly reprogrammed to implement multifunctionalities, offering a flexible platform for fundamental science and topological technologies. The chip integrates a large-scale silicon photonic lattice with microring resonators, allowing arbitrary control of structural parameters and geometrical configurations. It demonstrates robustness against weak disorders and counterintuitive topological Anderson phase transitions under strong disorders. The chip supports various topological phases, including Floquet TIs, and enables statistical analysis of topological robustness. It also demonstrates topological Anderson insulators and amorphous TIs. The chip's programmability allows for the realization of diverse topological lattices and the observation of statistical topological phenomena. The chip's reconfigurability and high controllability enable dynamic TPTs and robust topological edge modes. The chip's ability to withstand structural defects and its potential for large-scale integration make it a promising platform for future photonic technologies. The study highlights the importance of programmable photonic circuits in advancing topological photonics and its applications in fundamental science and technology.A programmable topological photonic chip is introduced, enabling precise control of light's topological phases through silicon photonic nanocircuits and microresonators. The chip allows individual programming of artificial atoms and their interactions, enabling dynamic topological phase transitions and diverse photonic topological insulators. It can be rapidly reprogrammed to implement multifunctionalities, offering a flexible platform for fundamental science and topological technologies. The chip integrates a large-scale silicon photonic lattice with microring resonators, allowing arbitrary control of structural parameters and geometrical configurations. It demonstrates robustness against weak disorders and counterintuitive topological Anderson phase transitions under strong disorders. The chip supports various topological phases, including Floquet TIs, and enables statistical analysis of topological robustness. It also demonstrates topological Anderson insulators and amorphous TIs. The chip's programmability allows for the realization of diverse topological lattices and the observation of statistical topological phenomena. The chip's reconfigurability and high controllability enable dynamic TPTs and robust topological edge modes. The chip's ability to withstand structural defects and its potential for large-scale integration make it a promising platform for future photonic technologies. The study highlights the importance of programmable photonic circuits in advancing topological photonics and its applications in fundamental science and technology.