Perhaps this is not what you think. When you use .Net Core MVC against a complete framework, it is true that the System.Web namespace exists and can be technically invoked, but it will not work the way you want. The reason is that the query pipeline for Asp.Net Core and System.Web is completely different. For example, when using Asp.Net Core MVC, if you check the HttpContext object from the moment the request arrives, it will be filled with all the information you expect, but if you check the current request using System.Web objects, you will see that they are not current request. This is because the current request did not come through the System.Web pipeline. He walked in through the .Net Core pipeline, if you like. Therefore, if you use .Net Core MVC, you will need to adhere to the tools and approaches to this structure, and not those presented in System.Web.
However, it should be possible to reference System.Web.dll if you really want to. If you are using VS2015, you will need to get a copy of System.Web.Dll and wrap it in a nuget package to establish a link to it. See .net core 1.0 visual studio linking to an external dll VS2017RC here has an alpha toolkit that should eliminate the need to wrap it in the NuGet package, but I had problems installing it my car, so I can not vouch for it personally.
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