Unfortunately, no. While corn kernels are generally considered to be edible, we would not advise allowing your cat to ingest the silk portion of the corn plant. Aside from the potential for stomach irritation, the stringy nature of the silk could cause an obstruction or other serious damage to the intestines, should it become bunched or bound up.
As you mention that your cat appears to be attracted to the silk, we would strongly recommend that you place your cat in a separate room when shucking fresh corn. You should also immediately dispose of the husks and silk in a bag or other trash receptacle in a location inaccessible to your cat, such as an outdoor trash bin.