Where are you seeing those points (e.g webapp, esri maps for sharepoint)) ??
You can use ArcGIS Desktop to transform those points in polygons. There are few ways to do that. Check this suppport technical article:
My suggestions or simple way is process the point data to be a polygon ( polygon shapefile - zip ) , before share in ArcGIS Online. Polygon is series on xy coordinates, not list of point objects. For example us use ArcMap , QGis, etc.
Shapefile sharing must include minimum of three files, .dbf, .shp. shx. Suggest .prj also. Find these files in the output location of your shapefile, zip them up and then post to sharepoint. Optionally, you may include all the shapefile extensions too.
Budur, looks like the shapefile suggestion won't work directly is sharepoint. Far as I can tell (I'm not an Esri ArcGIS for sharepoint expert) you've to have x, y and projection data as the source for sharepoint visualization. If you've used other tools/scripting to create the shapefile already, then you'll (probably) have to back up and export a table of the source data that includes the x, y and SRID data instead, then upload/ingest that into sharepoint.