We examine the capture of interplanetary dust particles by Saturn using both a simple two-dimensional code as well as a three-dimensional code with more detailed charging currents and forces. The incoming grain's energy may be lost to the magnetosphere due to the grain's finite charging time as it passes through the magnetospheric plasma. The two-dimensional code uses an equilibrium grain potential as a function of radial position and a charging time as a function of particle size. The ratio of prograde to retrograde captures depends on the shape of the equilibrium potential as a function of distance from the planet, with more prograde captures observed for more negative potentials. In the three-dimensional simulations, we observe a thick ring of dust particles captured into retrograde orbits. This dust, which has a typical size of 0.1 ¿m, forms a tenuous ring around the planet extending from the edge of the main rings to ≈9 planetary radii with a thickness of ≈3 planetary radii. We predict that the peak density for retrograde particles is 3 ¿ 10-15 cm-3, which should be observed by the Cassini spacecraft. We expect that with the appropriate viewing geometry, about 20 grains will be detected by the Cosmic Dust Analyzer during the first 4 years of the mission.