As of 1/2017, there is no way to do this, although ASP.NET Core is so fresh at that moment that I still hope for a newer and better answer.
The best way to create a single package of files for the ASP.NET Core website is to publish your application using dotnet publish and package the directory using the ZIP utility (or Octo.exe if you need the NuGet package for Octopus).
Current tools as of 2017/1: Octopack, which uses NuGet, cannot package .NET Core projects. NuGet itself is a minimal tool that requires a manifest or project file, and dotnet pack will only pack source files, not assets (see answer below for ways around this).
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