Yes you can.You need use Publish endpoint : http://resources.arcgis.com/en/help/arcgis-rest-api/#/Publish_Item/02r300000080000000/
So basically you need to upload service definition, csv or shapefile and execute publish operation. As a defult is becomes a private so you need to share it too if you need to. I think that this could be a bit better documented in a process vice.