.NET Core 3.1 Runtime is now generally available on Azure App Service for Windows and Linux applications. .NET Core is a cross platform version of .NET for building web apps, services and console apps.
While creating the App on Azure portal you can choose .NET Core 3.1 (LTS) option for both windows and Linux. See below screenshot for reference.
Fig: .NET Core 3.1 Runtime stack on Azure App Service
Note: If you are running your apps with .NET Core 3.0, you have to update to 3.1 version as 3.0 is going to end of life on March 3, 2020.
Check .NET Core Version on Azure Portal
If you are using windows based app service application, you can check your .NET Core version using the Console tab under Development tools. Click on Console tab and run dotnet --version to check your version and run dotnet --list-runtimes command to see all available run-times.
For Linux version, run command dotnet --list-runtimes using SSH tool under Development tools.