High-performance integrated spectrometers are highly desirable for applications ranging from mobile phones to space probes. Based on silicon photonic integrated circuit technology, we propose and demonstrate an on-chip speckle spectrometer consisting of a 15×15, 2D disordered microring lattice. The proposed 2D, disordered microring lattice was simulated by the transfer-matrix method. The fabricated device featured a spectral resolution better than 15 pm and an operating bandwidth larger than 40 nm. We also demonstrated that, based on the speckle patterns, our device can perform a spectrum classification using machine learning algorithms, which will have a huge potential in fast, intelligent material and chemical analysis.