In iOS, Xamarin.Forms resizes the screen when the keyboard comes up when the root node is a ScrollView. But when the root node is not a ScrollView
ScrollView
This Xamarin Forum question discusses it.
In addition if you want it in Android using Xamarin / Forms you can just set this in your main activity:
[Activity(WindowSoftInputMode = Android.Views.SoftInput.AdjustResize)] public class MainActivity ...