public Geometry Shape {get; set;}

      await QueuedTask.Run(() =>
      {
          //Don't use 'Shape'....Shape is the bounding box of the annotation text. This is NOT what you want...
          //
          //var insp = new Inspector();
          //insp.Load(annoLayer, oid);
          //var shape = insp["SHAPE"] as Polygon;
          //...wrong shape...

          //Instead, we must get the TextGraphic from the anno feature.
          //The TextGraphic shape will be the anno baseline...
          //At 2.1 the only way to retrieve this textLine is to obtain the TextGraphic from the AnnotationFeature
          QueryFilter qf = new QueryFilter()
          {
              WhereClause = "OBJECTID = 1"
          };

  //annoLayer is ~your~ Annotation layer

  using (var rowCursor = annoLayer.Search(qf))
  {
    if (rowCursor.MoveNext())
    {
      using (var annoFeature = rowCursor.Current as 
                  ArcGIS.Core.Data.Mapping.AnnotationFeature)
      {
        var graphic = annoFeature.GetGraphic();
        var textGraphic = graphic as CIMTextGraphic;
        var textLine = textGraphic.Shape as Polyline;
        // rotate the shape 90 degrees
        var origin = GeometryEngine.Instance.Centroid(textLine);
        Geometry rotatedPolyline = GeometryEngine.Instance.Rotate(textLine, origin, System.Math.PI / 2);
        //Move the line 5 "units" in the x and y direction
        //GeometryEngine.Instance.Move(textLine, 5, 5);

        EditOperation op = new EditOperation();
        op.Name = "Change annotation angle";
        op.Modify(annoLayer, oid, rotatedPolyline);
        op.Execute();
      }
    }
  }
});