Independent component analysis (ICA) is a general-purpose technique for analyzing multi-dimensional data to reveal the underlying hidden factors that are maximally independent from each other. We report the first photonic ICA on mixtures of unknown signals by employing an on-chip microring (MRR) weight bank. The MRR weight bank performs so-called weighted addition (i.e., multiply-accumulate) operations on the received mixtures, and outputs a single reduced-dimensional representation of the signal of interest. We propose a novel ICA algorithm to recover independent components solely based on the statistical information of the weighted addition output, while remaining blind to not only the original sources but also the waveform information of the mixtures. We investigate both channel separability and near-far problems, and our two-channel photonic ICA experiment demonstrates our scheme holds comparable performance with the conventional software-based ICA method. Our numerical simulation validates the fidelity of the proposed approach, and studies noise effects to identify the operating regime of our method. The proposed technique could open new domains for future research in blind source separation, microwave photonics, and on-chip information processing.