We designed and simulated a 1 GHz planar dipole antenna that is cloaked in a band around 10 GHz. Relative to an uncloaked antenna it has a reduced extinction cross-section for the co-antenna polarization, at the cost of an increased cross-polarization. This reduced extinction cross-section characterizes a reduction in scattering and absorption, and so reduced interference to electromagnetic waves in the frequency of cloaking. The dipole antenna element is cloaked by the introduction of sub-wavelength capacitive strips surrounding its length. The cloaking results were obtained using full wave simulations, showing for the realistic, lossy design a reduction of at least 5 dB in the extinction cross-section over a bandwidth of more than 1.5 GHz in comparison with the uncloaked antenna.