We propose and experimentally demonstrate a photonic measurement approach of microwave frequency with adjustable measurement ranges and low errors based on a silicon microring resonator (MRR). The key factor is that microwave photonic filters (MPFs) with high rejection ratios could be realized by a phase modulator, an optical filter, and a silicon MRR. In the experiment, by adjusting the wavelength of the laser diode, tunable MPFs with rejection ratios beyond 60 dB are realized in order to construct different amplitude comparison functions (ACFs) with high frequency resolutions (30 dB/GHz). According to the mapping relationships between the microwave frequency and power ratio of the ACF, the unknown microwave frequency could be measured. The experimental results show that microwave frequency could be measured from 10 to 19 GHz with a measurement resolution of 0.08 GHz. In the future, the measurement ranges and frequency resolutions could be manipulated according to the practical requirements. The photonic measurement method and compact device are significant in microwave systems.