We report on the investigation and implementation of a lumped-component, radio-frequency resonator used in a cryogenic vacuum environment to drive an ion trap. The resonator was required to achieve the voltages necessary to trap (~100 V), while dissipating very little power. Ultimately, for an input voltage of 1.35 V, a voltage gain of 100 was measured at 5.7 K, using a design which dissipated only 18 mW. The resonator operated at a frequency of 7.64 MHz and had a Q of 700. Single (40)Ca(+) ions were confined in a trap driven by this device, providing proof of successful resonator operation at low temperature.