A laser tweezer (LT) along with advanced imaging techniques has been widely applied to manipulate and study living as well as nonliving microscopic objects. In this study we present yet another novel application of LTs for a precise measurement of the viscosities of fluids in a micro-volume flow. We have demonstrated this novel application by measuring the viscosity of a fetal bovine serum (FBS) using a LT constructed from a single intensity gradient laser trap. By calibrating the LT using dielectric silica micro-beads in a fluid with a known viscosity, specifically water, and by suspending same size of silica beads in the FBS and trapping with the same trap, we have determined the viscosity of the FBS at different temperatures. We have used the relationship between the trapping and Stoke's drag force for a constant drag speed to determine the viscosity. We have also analyzed the viscosities determined in comparison with corresponding viscosities measured using an Ostwald viscometer.