I’m assuming you’ve already enabled a system-assigned or user-assigned identity for this. If so, all you need to do is execute the following commands in your database:
-- Create the user
CREATE USER [functionappname] FROM EXTERNAL PROVIDER;
-- Grant permissions READ/WRITE
ALTER ROLE db_datareader ADD MEMBER [functionappname];
ALTER ROLE db_datawriter ADD MEMBER [functionappname];
This grants read and write permissions to the user, though you can add more roles if needed.
That’s it!