<telerik:RadTemplatedPicker x:Name="picker"
                            Placeholder="Select a Date"                                    
                            PickerMode="Popup">
    <telerik:RadTemplatedPicker.SelectorTemplate>
        <ControlTemplate>
            <telerik:RadCalendar x:Name="calendar" SelectedDate="{TemplateBinding SelectedValue, Mode=TwoWay, Converter={StaticResource StringToDateTimeConverter}}" />
        </ControlTemplate>
    </telerik:RadTemplatedPicker.SelectorTemplate>
</telerik:RadTemplatedPicker>

public class StringToDateTimeConverter : IValueConverter
{
    public object Convert(object value, Type targetType, object parameter, CultureInfo culture)
    {
        return value;
    }

    public object ConvertBack(object value, Type targetType, object parameter, CultureInfo culture)
    {
        if (value is DateTime selectedDate)
        {
            return selectedDate.ToString("yyyy/MMM/dd");
        }
        return null;
    }             
}