Absorption spectroscopy is widely used in sensing and astronomy to understand remote molecular compositions. However, dispersive techniques require multichannel detection, reducing detection sensitivity while increasing instrument cost when compared to spectrophotometric methods. We present a novel non-dispersive infrared molecular detection and identification scheme that performs spectral correlation optically using a specially tailored integrated silicon ring resonator. We show experimentally that the correlation amplitude is proportional to the number of overlapping ring resonances and gas lines, and that molecular specificity can be achieved from the phase of the correlation signal. This strategy can enable on-chip detection of extremely faint remote spectral signatures.