A new method for the synthesis of uniform silver nanoparticles using a single silver reduction step is presented. Fine control over the nanoparticle's size is achieved by varying the concentration of tannic acid, one of the reducing agents, resulting in uniform nanoparticles in the range of 18 nm to 30 nm in diameter with a standard deviation of less than 15%. Changes in the optical properties of the nanoparticles are correlated with their diameter. As the diameter increases the absorption peak is red-shifted. Specifically, for six different sizes of nanoparticles, ranging from 18 nm to 30 nm in diameter, a red-shift from 401 nm to 410 nm in the absorption peaks is measured. In addition, the extinction coefficient increases as the third power of the nanoparticle radius. Rhodamine 123 adsorbed to 30 nm silver nanoparticles exhibits characteristic Raman spectrum suggesting that these nanoparticles are efficient substrate for surface-enhanced Raman spectroscopy.