While OnSong is able to view and display PDF, PNG, JPEG, Microsoft Word, and other similar types of chord charts, OnSong is designed to work best with plain-text-based chord charts made in programs like TextEdit for Mac or Notepad for Windows. PDF chord charts are more like a photograph and actually contain no actual text that can be recognized or edited. Because of this, OnSong cannot format songs, detect keys, and perform other OnSong functions like Low Light Mode in PDF files. These files are unfortunately only able to be viewed "as-is".
OnSong does contain an "Extract Text" option that might be of some use. If you use the Extract Text feature in the Conversion Toolbar of the Song Editor, OnSong will attempt to scan your song and perform optical character recognition, which can often have mixed results- sometimes chords or lyrics might become misplaced or scrambled around. However, once the text is extracted and you are able to take some time to reformat and "clean up" the song, you will now be able to view the song as a text file and make edits like detecting/changing keys or capos, highlighting chords, resizing text, etc.
Conversely, if you'd like to create your songs using TextEdit or Notepad, you can follow the guidelines listed here to make sure that your song is in optimal OnSong format: http://onsongapp.com/docs/features/formats/onsong/