You can fax your ballot or other voting document by using the special faxing service through the Federal Voting Assistance Program (FVAP.gov). You will need to email your ballot or any other voting matter and all required supporting materials (see your state’s instructions) to email@example.com along with the FVAP fax transmission coversheet here (scroll to the bottom of the page). FVAP will then fax your election materials to your Local Election Office. You should later verify that they were received OK with your Local Election Office.
Alternatively you can fax a document or photo from your smart phone too. For Android phones, see here (the app FaxFile has been recommended by a friend); for iPhone’s, look here or just search on something like “send fax iPhone free” and you’ll find some.