We demonstrate on-chip laser absorption spectroscopy using silicon microring resonators integrated with PDMS microfluidic channels. A 100 microm radius microring resonator with Q > 100,000 is used to enhance the interaction length between evanescent light and a cladding liquid. We measure absorption spectra of less than 2 nL of N-methylaniline from 1460 nm to 1610 nm with 1 nm resolution and effective free space path lengths up to 5 mm. This work can help realize a completely on-chip spectroscopy device for lab-on-a-chip applications.