The dynamical nature of biomolecular systems means that knowledge of their viscoelastic behavior is important in fully understanding function. The linear viscoelastic response can be derived from an analysis of Brownian motion. However, this is a slow measurement and technically demanding for many molecular systems of interest. To address this issue, we have developed a simple method for measuring the full linear viscoelastic response of single molecules based on magnetically driven oscillations of an atomic force microscope cantilever. The cantilever oscillation frequency is periodically swept through the system resonance in less than 200 ms allowing the power spectrum to be obtained rapidly and analyzed with a suitable model. The technique has been evaluated using dextran, a polysaccharide commonly used as a test system for single molecule mechanical manipulation experiments. The monomer stiffness and friction constants were compared with those derived from other methods. Excellent agreement is obtained indicating that the new method accurately and, most importantly, rapidly provides the viscoelastic response of a single molecule between the tip and substrate. The method will be a useful tool for studying systems that change their structure and dynamic response on a time scale of 100-200 ms, such as protein folding and unfolding under applied force.