I'm fairly sure it's not currently possible to set the "content source URL" when creating posts with the API.
(Unless there is some POST variable I am unaware of, that is not documented ? )
Any chance that this will be added to the API? It's really a pain that you have to go to the post on Tumblr.com to edit it, and add the Source URL for any posts you make with the API.
Even on Photo posts, when specifying the "source" for the Photo as a URL, the post created with the API does not set the "content source url" to the URL you used for the photo.
Thanks,
Felix