The quickest way in Azure SQL is to use BULK operation (BULK INSERT or OPENROWSET BULK). You need to create an EXTERNAL DATA SOURCE in first place pointing to the Azure Blob Storage that contains the CSV you want to import, and then you can use BULK operation:
SELECT * FROM OPENROWSET(BULK ...)
A full explanation and sample is here:
https://medium.com/@mauridb/automatic-import-of-csv-data-using-azure-functions-and-azure-sql-63e1070963cf
the example describe how to import files dropped in a Blob Storage. Multiple file will be imported in parallel.
For a complete description of how to bulk import data from Azure Blob Storage to Azure SQL, there are a lot of samples in the official documentation
https://learn.microsoft.com/en-us/sql/t-sql/statements/bulk-insert-transact-sql?view=sql-server-2017#f-importing-data-from-a-file-in-azure-blob-storage
Another option is to use Azure Data Factory that will be as fast as using the BULK option just mentioned, but it requires the creation of an Azure Data Factory pipeline that adds some complexity to the solution...but, on the other hand, can be done without writing a single line of code.