Arun Sirpal shows how to use Azure Automation to rebuild indexes on an Azure SQL Database database:
The answer is via Azure Automation.
At a high level this is what I did.
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Create an Automation Account. 
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Create a credential. 
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Create a PowerShell Runbook which has the code for index rebuilds. 
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Create a schedule and link it to the above. 
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Configure parameters within the schedule (if any). 
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Configure logging level (if desired). 
Click through for the detailed steps.