The rapidly fluctuating magnetic field should generate a rapidly fluctuating electric field which propagates away from the wire at the speed of light. I'm not sure how rapidly current can be switched in a wire, but perhaps radio waves could be generated in this way? This probably would not be a cost effective way to generate light but I am curious if we could.
Visible light cannot be generated using switched or oscillating currents with today's technology.
I believe that THz radiation, with wavelengths on the order of 0.1 to 1 mm, is the closest that has been generated using high frequency currents. This band is also called submillimeter radiation, and barely reaches the far infrared range. Various high frequency RF, microwave and millimeter wave techniques have been used to generate THz radiation, including backward wave oscillators (BWO), gyratrons, and frequency multipliers using diodes or varactors.
In addition, laser based techniques such as photomixing and photconductive switching have been used. Photomixing uses two IR lasers with separate frequencies illuminating a semicondutor that produces a difference frequency in the THz range by conductivity modulation.
Photoconductive switching uses a laser generated, compressed, short optical pulse on the order of a femtosecond, applied across a small gap between conductors bridged by a semicondutor to produce a current pulse. The resulting current either exites an antenna directly, or is applied to a device to be tested. Another photoconductive device can be used as a detector. This technique is used in time-domain spectroscopy for study of material properties in the terahertz range.
The power level generated by these techniques is generally quite small ($\mu$W, or lower), so their practical use is limited.
Generally, the size of the system that produces an EM wave is comparable to the wavelength of the wave. Radio waves come from antennas measured in meters, microwaves from resonant cavities measured in centimeters, light from electron orbitals, and gamma waves from nuclei. A circuit and antenna to produce light would have to be the size of a molecule. Its frequency would be limited by the speed of light.
This question is related to an area of study known as plasmonics, which is the coupling of light to a solid-state version of a plasma. This phenomenon is responsible for the differences in colors between silver, gold, and copper, which is related to differences in the naturally resonant frequency of the electrons in these metals' free-electron gas plasmas.
While good methods for producing light at visible wavelengths through externally applied oscillating electric fields don't exist, plasmonics does provide for the modification of the properties of light through the temporary creation of plasmons, oscillations in the density of free electrons at the frequency of the incident radiation, which can in turn be coaxed to reradiate as other forms of light (for example, in a different direction, or at a different frequency). A large field of study is devoted to the development of plasmonic nano-antennae and other types of plasmonic nanomaterials. At slightly longer wavelengths, in the terahertz regime (but much shorter than conventional radio frequency wavelengths), researchers have proposed devices to perform the direct conversion of A/C electric field to light waves.