We have devised an analytical and sorting system combining optical trapping with Raman spectroscopy in microfluidic environment, dedicated to identification and sorting of biological objects, such as living cells of various unicellular organisms. Our main goal was to create a robust and universal platform for non-destructive and non-contact sorting of micro-objects based on their Raman spectral properties. This approach allowed us to collect spectra containing information about the chemical composition of the objects, such as the presence and composition of pigments, lipids, proteins, or nucleic acids, avoiding artificial chemical probes such as fluorescent markers. The non-destructive nature of this optical analysis and manipulation allowed us to separate individual living cells of our interest in a sterile environment and provided the possibility to cultivate the selected cells for further experiments. We used a mixture of polystyrene micro-particles and algal cells to test and demonstrate the function of our analytical and sorting system. The devised system could find its use in many medical, biotechnological, and biological applications.