Since you mentioned Web API's. I am not sure if you are particularly interested in JS API. As Rickey mentioned that map rotation will be available with the final release of JS API 4.0 which would be some time next year. Currently, it is in beta.
If you really need this functionality it is currently available wit ArcGIS API for Silverlight as demoed in this sample
ArcGIS API for Silverlight - Interactive Samples | ArcGIS for Developers
Just so you know our Silverlight API will be deprecated sometime late next year.
Jeff,
I know that it works with JS 4.0 which is still in beta
Easy navigate the viewpoint and camera in 3D map | ArcGIS API for JavaScript
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