RStudio Server Pro is now available on the Azure Marketplace, the company announced on the RStudio Blog earlier this month. This means you can launch RStudio Server Pro on an virtual machine with the memory, disk, and CPU configuration of your choice, and pay by the minute for the VM instance plus a the RStudio software charge. Then, you can use a browser to access the remote RStudio Server (the interface is nigh-indistinguishable from the desktop version), with access to the commercial features of RStudio including support for multiple R version and concurrent R sessions, load-balancing and high availability instances, and enhanced security.
RStudio Server Pro and Microsoft R Server are both very nice for production-quality R servers. You can get away with the open source versions, but there are some good reasons to use the enterprise-grade products in an enterprise.