In this paper we investigate the implementation of single-qubit operations in the Kane solid-state quantum computer by Rabi flipping the nuclear qubits via the application of resonant radio-frequency fields. Specifically, we calculate the change in the resonance frequency of the nuclear qubits with the application of electric potentials to metallic control gates designed to address individual qubits, as well as the effects these fields have on neighbouring qubits. We find that although the resonance frequencies of the neighbouring qubits are shifted, it is still theoretically possible to implement single-qubit operations with the fidelity required for large-scale quantum computation using this technique.