In this study, polyelectrolyte (PE) layers are deposited on substrates made by glass covered with an array of gold nanoparticles (GNPs). In particular, the samples studied have 0 PE layers (GGPE0), 3 PE layers (GGPE3), 11 PE layers (GGPE11), and 21 PE layers (GGPE21). All samples have been studied by micro-Raman spectroscopy. An acetic acid solution (10% v/v) has been used as a standard solution in order to investigate the SERS effect induced by different numbers of PE layers in each sample. The Surface Enhancement Raman Spectroscopy (SERS) effect correlating to the number of PE layers deposited on the samples has been shown. This effect is explained in terms of an increase in the interaction between the photon of the laser source and the plasmonic band of the GNPs due to a change of the permittivity of the surrounding medium around the GNPs. The trends of the ratios of the intensities of the Raman bands of the acetic acid solution (acetic acid and water molecules) on the band at 1098 cm−1 ascribed to the substrates increase, and the number of PE layers increases.