To add scrollbars to ItemsControl you have to modify the control template and to add ScrollViewer for the ItemsPresenter.
Xaml
<ItemsControl >
<ItemsControl.Template>
<ControlTemplate>
<ScrollViewer x:Name="ScrollViewer" Padding="{TemplateBinding Padding}">
<ItemsPresenter />
</ScrollViewer>
</ControlTemplate>
</ItemsControl.Template>
</ItemsControl>