In this study, 4-mercaptobenzoic acid (MBA)-Au nanorods conjugated with a GPR120 antibody were developed as a highly sensitive surface-enhanced Raman spectroscopy (SERS) probe, and were applied to detect the interaction of fatty acids (FA) and their cognate receptor, GPR120, on the surface of human embryonic kidney cells (HEK293-GPRR120) cultured in a polydimethylsiloxane (PDMS) microfluidic device. Importantly, the two dominant characteristic SERS peaks of the Raman reporter molecule MBA, 1078 cm−1 and 1581 cm−1, do not overlap with the main Raman peaks from the PDMS substrate when the appropriate spectral scanning range is selected, which effectively avoided the interference from the PDMS background signals. The proposed microfluidic device consisted of two parts, that is, the concentration gradient generator (CGG) and the cell culture well array. The CGG part was fabricated to deliver five concentrations of FA simultaneously. A high aspect ratio well structure was designed to address the problem of HEK cells vulnerable to shear flow. The results showed a positive correlation between the SERS peak intensity and the FA concentrations. This work, for the first time, achieved the simultaneous monitoring of the Raman spectra of cells and the responses of the receptor in the cells upon the addition of fatty acid. The development of this method also provides a platform for the monitoring of cell membrane receptors on single-cell analysis using SERS in a PDMS-based microfluidic device.