I have made a base map by georeferencing an old map on ArcMap Desktop, but how do I import that onto the online version and use it on a web map?
If you are looking to add the map as a basemap in AGOL, you might like to start with creating a tiled map service.
Publish a Tiled Service to ArcGIS Online w/o ArcGIS for Server or Utilizing Your Credits
Then add the layer as a basemap to the webmap of AGOL.
Using Custom Basemaps
Retrieving data ...