Updated June 2020
It is no longer possible... allegedly. If you have a Facebook or Instagram dedicated contact (because you work in either a big agency or with a big client) it may potentially be possible depending on your use case, but it's highly discouraged.
Before December 2019:
It is now "possible":
https://developers.facebook.com/docs/instagram-api/content-publishing
The Content Publishing API is a subset of Instagram Graph API endpoints that allow you to publish media objects. Publishing media objects with this API is a two step process — you first create a media object container, then publish the container on your Business Account.
Its worth noting that "The Content Publishing API is in closed beta with Facebook Marketing Partners and Instagram Partners only. We are not accepting new applicants at this time." from https://stackoverflow.com/a/49677468/445887