Update 09.08.2018
Unity is being developed here but I haven\'t had the time to test how it plays with the ASP.NET Core framework.
Update
For ASP.Net Core 2.0, 2.1, 2.2, 3.1 and Unity there is official solution available from Unity authors as NuGet package here: NuGetPackage
Here is Git repository with samples: Git repo
Usage is very simple (from Git repo homepage):
public static IWebHost BuildWebHost(string[] args) =>
WebHost.CreateDefaultBuilder(args)
.UseUnityServiceProvider() <---- Add this line
.UseStartup()
.Build();
And here is example with Unity DI for ASP.Net Core.
I am using this solution in my ASP.Net Core application and works good.