Single chip integrated spectrometers are critical to bring chemical and biological sensing, spectroscopy, and spectral imaging into robust, compact and cost-effective devices. Existing on-chip spectrometer approaches fail to realize both high resolution and broad band. Here we demonstrate a microring resonator-assisted Fourier-transform (RAFT) spectrometer, which is realized using a tunable Mach-Zehnder interferometer (MZI) cascaded with a tunable microring resonator (MRR) to enhance the resolution, integrated with a photodetector onto a single chip. The MRR boosts the resolution to 0.47 nm, far beyond the Rayleigh criterion of the tunable MZI-based Fourier-transform spectrometer. A single channel achieves large bandwidth of ~ 90 nm with low power consumption (35 mW for MRR and 1.8 W for MZI) at the expense of degraded signal-to-noise ratio due to time-multiplexing. Integrating a RAFT element array is envisaged to dramatically extend the bandwidth for spectral analytical applications such as chemical and biological sensing, spectroscopy, image spectrometry, etc.