It is one of the basic concepts of Newtonian fluid dynamics that at low Reynolds number (Re) the Navier-Stokes equation is linear and flows are reversible. In microfluidic devices, where Re is essentially always low, this implies that flow resistance in microchannels is isotropic. Here we present a microfluidic rectifier: a microscopic channel of a special shape whose flow resistance is strongly anisotropic, differing by up to a factor of 2 for opposite flow directions. Its nonlinear operation at arbitrary small Re is due to non-Newtonian elastic properties of the working fluid, which is a 0.01% aqueous solution of a high molecular weight polymer. The rectifier works as a dynamic valve and may find applications in microfluidic pumps and other integrated devices.