The Kentico Xperience API does not directly support this for dot net core according to my understanding. However, if your dot net core live site is exposed directly to the internet (no proxy in the way), then the standard C# code samples should work. Typically via code that includes the ForwardHeaders and then using HttpContext to return the IP. See this documentation from Microsoft. Once that is hooked up you should then be able to use this in a Controller.
var remoteIpAddress = Request.HttpContext.Connection.RemoteIpAddress;