Any Instagram photo you take will be automatically saved in your Dropbox Camera Uploads folder (under Instagram folder). This way you can backup your Instagram. I use this to upload my photos to Google+ every once in a while.
Then
Add file from URL
This Action will download a file at a given URL and add it to Dropbox at the path you specify. NOTE: 30 MB file size limit.
Discover more time saving integrations for Instagram and Dropbox