Providing that your app is developed on Android, I feel that Google Drive would be the best option. For a user to have an Android device, they are required to have a Gmail account and this is also merged with Google Drive. Google Drive is actually made for storing files, unlike other ways of doing this, like asking the user to email the file to themselves where the file is actually only saved as an attachment.
I'd then use a sharing Intent
like so:
Intent shareIntent = new Intent(Intent.ACTION_SEND);
You could even map this straight to launching Google Drive by using the Google Drive's app package name. If you do choose to use share Intent
s and want to specifically map the user to only using Google Drive to upload the file instead of letting them choose, for reference, here's the package name for Google Drive:
com.google.android.apps.docs