Please consider adding that table to a Sync Group between the on-premises database and the Azure SQL database using Azure SQL Data Sync. You can configure a manual sync or an automated sync with intervals for syncing that range from seconds to days. SQL Data Sync tool is free.
Using linked servers for that purpose should result in poor performance and long running job when there is a considerable number of rows to send to Azure SQL. That job you mentioned cannot recover from transient errors as SQL Data Sync does.