Open ArcGlobe. Add the annotation features to ArcGlobe and select the option to 'Display features as 3D vectors'. Accept all other defaults and click Finish.
Right-click the annotation layer, and select Properties. Click the Elevation tab.
For the Offset property, enter a value, in meters from sea level, appropriate to the area of interest.
Note: Alternatively, an elevation dataset can be used in ArcGlobe. By default, ArcGlobe is flat. If there is no elevation dataset, use the following dataset from the ESRI Data & Maps, Elevation and Image Data - World: world_elevation\gtopo30\gtopo_1km. Add this dataset as an elevation layer. This layer does not need to be cached.
Save the globe document as a 3DD file.
Go to the Tools menu > Options in ArcGlobe. Click on the Cache tab in the Options dialog box.
Set the cache path to the same directory as the ArcGIS Server cache directory (C:\arcgisserver\arcgiscache by default). Click OK to close the Options dialog box.
Right-click on the annotation layer in the Table of Contents in ArcGlobe, and select Generate Data Cache. Click OK to generate the globe cache.
Close ArcGlobe. Save the changes to the globe document.