Follow these steps to deploy it successfully:
1. Go to Azure manage portal, then hit the new button, after that click on compute and select Web app, and press the Quick create option.
2. Once you click on the Web App, you will able to see your webiste.
3. After that, select your local git repository.
I hope this will help.
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Want to know more about deploying a Web App on Azure? Watch this video on Learning Azure -3 | Deploying End to End Website on Azure :