I have downloaded FontAwesome using npm and then copied the css-file and the fonts into the right folders in the root-diretory of my electron-application using grunts copy t
In my situation, Git was treating the file as a text file, and messing with its "line endings". This was corrupting the file.
Adjusting the .gitconfig to recognize *.woff files as binary, then removing the file, and adding a new copy from https://github.com/FortAwesome/Font-Awesome/raw/v4.2.0/fonts/fontawesome-webfont.woff solved the issue for me.