how can you upload files to an Azure Web Apps virtual directory?

From the Kudu powershell console, if you open a folder in the file browser, you can drag and drop a zip file into it. It's not obvious until you drag the file over top of the file explorer at which time a box opens up over the size column that says "Drag here to upload and unzip".

You can set the FTP credentials on the Deployment credentials blade within your App Service:

However, the easiest way is to upload your files using the KUDU console. To access the console navigate to https://<yoursite>.scm.azurewebsites.net where <yoursite> is the name of your App

In the Kudu console, click on the Debug Console tab, then on PowerShell. That will open a file browser where you can navigate to your directory and upload the files by dragging and dropping the files into the browser window:

1. Go to YOURSITE.azurewebsites.net/ZipDeployUI
   
2. Drag and drop

Note: all files and folders in current wwwroot will be removed without warning

I used Visual Studio IDE. Access the Publish interface as shown below.

• Click Manage in Cloud Explorer it will open the specified Azure App web service. Drill down to Files>wwwroot and right click then select Upload File

Hopefully it works for your case.