Azure SQL Database, the database-as-a-service based on Microsoft SQL Server, now offers R integration. (The service is currently in preview; details on how to sign up for the preview are provided in that link.) While you've been able to run R in SQL Server in the cloud since the release of SQL Server 2016 by running a virtual machine, Azure SQL Database is a fully-managed instance that doesn't require you to set up and maintain the underlying infrastructure. You just choose the size and scale of the database you want to manage, and then connect to it like any other SQL Server instance. (If you want to learn how to set up an Azure SQL database, this Microsoft Learn module is a good place to start.)
You can find detailed documentation on using the R integration here, where you can learn how to apply R functions to tables from a stored procedure, execute R from a local RStudio client on the remote database, and add new R packages to the R instance in the SQL database. The interface is the same as for standalone SQL instances (with the exception that Python is not yet supported on Azure SQL Database), so the tutorials and guides there apply here as well.
For more details on the new R integration on Azure SQL Database, including how to sign up for the preview, check out the blog post at the link below.