Impedance loading of antennas has been of interest for more than half a century due to its ability to fundamentally change an antenna's operating characteristics. Variable reactive loading can be employed for configurability of the frequency response, polarization and far-field properties of an antenna. Closed-form expressions for the current and input impedance of a thin-wire loop antenna with loads in the periphery were derived in the RF and optical regimes in 1965 and 2017, respectively. Meanwhile, closed-form far-field radiation properties of circular loop antennas in the RF and optical regimes were derived in 1996 and 2017. This paper extends this theory to provide closed-form analytical expressions for the far-field radiation properties of impedance-loaded loop antennas valid from the RF to the optical regimes. The expressions are validated by comparison with commercial simulation tools. In addition, a beam steering example is presented as a potential application of the theory.