The best way to do this is to add a Connection String from the Azure portal:
- From your Function App UI, click Function App Settings
- Settings / Application Settings
- Add connection strings
They will then be available using the same logic as if they were in a web.config, e.g.
var conn = System.Configuration.ConfigurationManager
Or if you're using a non-.NET language, you can use App Settings instead, which become simple environment variables at runtime that your functions can access.