SQL Server and Azure, both are (very popular) products of Microsoft, why won't they integrate them both to create another "popular" product? :-) However, you do not "create SQL Server", on a cloud, you can surely get a subscription for a service and use it in your online hosted web application (
if that is what you need!) and then provide services in your desktop applications.
SQL Server is available on Azure as a PaaS (
platform-as-a-service) so that you can get a subscription for an SQL Server instance for your web application. There are many tools and ways to integrate that service in your own web application. Read the following resources:
SQL (PaaS) Database vs. SQL Server in the cloud on Azure VMs (IaaS) | Microsoft Azure[
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Provision a SQL Server virtual machine | Microsoft Azure[
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How to use SQL Database (.NET) | Microsoft Azure[
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