Short answer: It is not (yet) possible
Long answer (Coming directly from Instagram folks) :
At this time, uploading via the API is not possible. We made a conscious choice not to add this for the following reasons:
- Instagram is about your life on the go – we hope to encourage photos from within the app. However, in the future we may give whitelist access to individual apps on a case by case basis.
- We want to fight spam & low quality photos. Once we allow uploading from other sources, it’s harder to control what comes into the Instagram ecosystem. All this being said, we’re working on ways to ensure users have a consistent and high-quality experience on our platform.
So in conclusion: you can upload content to Instagram only within Instagram. Any other external source, like for example WordPress, can not upload and/or sync with Instagram