Desktop applications typically run on a desktop. What precisely are you trying to do with the desktop application in the cloud? If it is accessing a SQL Server database and uses a middle-tier application server, perhaps those two “server-side” layers can be moved to cloud. But more detail is needed.
Are are you simply trying to run an app created for desktop on cloud servers for some reason? Then the answer is yes, you can run desktop apps on Azure servers, as long as it supports command line parameters and can do its thing via command-line only.