Connecting to on-prem SQL Server through Azure Databricks

You can use the JDBC drivers as scsimon suggested.

However, unless your database is accessible to the internet it will be unable to connect.

To resolve this you need to vnet attach your databricks workspace to a vnet that has VPN or ExpressRoute connectivity to your onprem site (and correct routing in place). This is currently a preview feature that you will need to contact Microsoft to get enabled.

Full details here: https://docs.azuredatabricks.net/administration-guide/cloud-configurations/azure/vnet-inject.html