Here are some options to do what you want to do.
If you have ArcGIS Server, you could host this data yourself in a map service. If you don't, all you can do at this point with ArcGIS Online (ArcGIS.com is the website that represents ArcGIS Online) is manually draw your data over the map (when viewing a map, you can "Create an editable layer").
As I mentioned in an earlier post, we are working on the ability to add data over the map without having your own ArcGIS Server, but that functionality is not available yet.
Thanks,
Mike