No, it is not possible to import a symbol from ArcMap to ArcGIS Online. ArcGIS Online does not have the ability to import symbology from ArcMap. To symbolize the features with the desired symbol, edit the features in ArcMap and publish it to ArcGIS Online.
Publish the file as a service instead of a map package to maintain the symbology defined in ArcMap.
In some cases, the symbols in a published feature service are downgraded in ArcGIS Online because the symbols are not supported. As an alternative, to symbolize the layer with a customized symbol in ArcGIS Online, use a JPEG, GIF, or PNG file, host the image on an image sharing site, and use the link as a custom image.