If you want to allow the user to launch the Windows Phone Store and display the rate and review page for the current app , you can use the Windows.System.Launcher.LaunchUriAsync method by passing the right handle .

In the Windows Phone 8 and earlier version , the developers could use the MarketplaceReviewTask but with Windows Phone 8.1 (Windows Runtime App) , the developers can utilize the Launcher class which allows the developers to use the LaunchUriAsync and launch the built-in apps .

How to Launch the Rate and Review Page from Windows Phone 8.1 App ?

Below is a sample code snippet that uses the Windows.System.Launcher.LaunchUriAsync method to launch the Rate and Review Page from the Windows Phone App.

async private void Button_Click(object sender, RoutedEventArgs e)
{
  await Windows.System.Launcher.LaunchUriAsync(
        new Uri("ms-windows-store:reviewapp?appid=" + CurrentApp.AppId));
}