Deploy Vue.js App as Azure App Service from Visual Studio Code

Please refer to the Local Git Deployment as per the Microsoft Docs.

Failing that, you could try to deploy manually via FTP. You can do that by going to your Azure Portal:

App Service => Deployment Center => FTP => Dashboard

You'll then find some FTPS credentials on that page and all you have to do is deploy your dist folder up to /site/wwwroot, see more here.