Summary form only given. Raman spectroscopy has become a powerful tool for microscopic analysis of organic and biological materials. When combined with Optical Tweezers, it allows investigating of a single, selected micrometric particle in its natural environment, therefore, reducing unwanted interferences from the cover plate. A general problem affecting either Raman spectrometers than Raman Tweezers systems is the background contribution coming from the environment surrounding the sample under investigation. This drawback is usually overcome by subtracting the acquired spectrum from a reference spectrum. In this work we report on a novel method which allows acquiring Raman spectra of trapped particles (polystyrene microspheres) free from any background contribution and without any subtraction procedure. The method is based on the use of two collinear and co-propagating laser beams: one is devoted to trapping (trapping laser), and a second one is used to excite the Raman transitions (pump laser). The trapping laser, by means of a galvomirror, moves periodically the trapped particle back and forth along one direction perpendicular to the propagation axis at a given frequency. The scattered photons are collected through the same focusing objective and spectrally analysed by means of spectrometer; the Stokes photons are then detected by a photomultiplier, and the signal sent in a lock-in amplifier for a phase-sensitive detection scheme. The purpose of the present work is to furnish a detailed description of our method and to supply a systematic study concerning the formation of the Raman signal. The results found demonstrate that this method may find valuable applications in rapid sensing of biological samples in aqueous solutions. One of the potential applications lies in studying the diffusion of molecules into micro-sized particles. This kind of application is being carried out in our laboratory.