How can I Schedule a Sql job in Microsoft Azure SQL database?

Since this question was first asked, there is now another alternative to handle this problem:
Azure Functions

Here are a couple of examples that could easily be modified to call a stored procedure that rebuilds your indexes

• Create a function in Azure that is triggered by a timer
• Use Azure Functions to connect to an Azure SQL Database

Also see

• How to maintain Azure SQL Indexes and Statistics - this page has an example stored procedure for rebuilding your indexes that you can download.
• Reorganize and Rebuild Indexes

A few things to keep in mind with Azure functions

• They are built on top of Azure Web Jobs SDK and offer additional functionality
• There are two different pricing models:
  • App Service plan (attach it to an existing plan)
    • Predictable cost model
    • It puts extra load on the same VM used by your web site
  • Consumption plan
    • You get some free processing every month
    • The default maximum run time is 5 minutes to prevent billing problems, but it can be changed via the host.json file.

Edit September 5, 2021 to add additional information

It should be noted that if you need SQL Agent, you have another option now. I would suggest reading up on Azure SQL Managed Instances. You can see a comparison of Azure SQL to Azure SQL Managed instance here in the Microsoft Documentation. With Azure SQL Managed Instances, your transition to the cloud could be a lot simpler since a lot of the on-premise features you are used to are already there (including SQL Server Agent, DB Mail, etc.).

This feature has been rejected by Microsoft, see here.

To quote the post:

Today in Azure there are several alternatives,

1) SQL Database Elastic Jobs http://azure.microsoft.com/en-us/documentation/articles/sql-database-elastic-jobs-overview/

2) The Azure job scheduler http://www.windowsazure.com/en-us/services/scheduler/

3) The new preview of Azure Automation http://azure.microsoft.com/en-us/services/automation/.

4) SQL Server in a VM

Option 1 requires an additional dedicated cloud service, which increases cost. Option 2 is free (I think) as long as you don't run more than once per hour.

Azure SQL does not support sql jobs. From documentation:

Microsoft Azure SQL Database does not support SQL Server Agent or jobs. You can, however, run SQL Server Agent on your on-premise SQL Server and connect to Microsoft Azure SQL Database.

WebJobs: If you have a website you can create webjob and run it on schedule. See more here

Other alternatives - Scheduling job on SQL Azure