I would use the Azure Scheduler. If your are familiar with a Cron job, this is very similar. All the Azure Scheduler does is make a REST call to an end point on a schedule. This would probably be more cost affective then setting up a worker role. Also, I would make sure to take into account security when setting up the Azure Scheduler. I would pass some type of secret to the API as a parameter so that it's not open to anonymous calls (although technically it would be.) If you want to execute certain tasks during the call, then I would store them in a table in your database. The worker role came before the Azure Scheduler, so the worker role lost in my book when the scheduler was made public.
UPDATE:
Another thought, is to look into the automation option in Azure: https://msdn.microsoft.com/library/azure/dn643629.aspx
With this option you can execute PowerShell scripts:
http://azure.microsoft.com/blog/2014/08/20/azure-automation-capabilities-in-depth-the-azure-automation-powershell-cmdlets/