Hi,
I wonder if I can stretch my on-premise database to SQL Server in Azure VM.
No you cannot use the build-in Stretch Database feature (but you have other options)
You can stretch you database in the virtual machine to Azure SQL Database
Stretch Database is a feature that Stretch the database to Azure SQL Database.
SQL Server on Virtual machine is just like SQL Server on premises in this case
Note: You can use Big Data Clustered with your on-premises server and you Virtual Machine Server.