I dont see an API available to create GitHub Organization via REST API v3. However i can only see it enabled at user level (Click on the + button -> Create Organization)
I was going through the API documentation and i could’nt find it: https://developer.github.com/v3/orgs/
We requrie it on Enterprise GitHub (currently we are on v2.16.4 ). Please let us know if this is a feature planned for a future release.