要访问日历，您可以使用Calendar类，它在 Delphi 中由JCalendar类表示。
您可以找到一组样本here
这是一个 Delphi 的例子

uses
  Androidapi.JNI.GraphicsContentViewText,
  FMX.Helpers.Android,
  Androidapi.JNI.JavaTypes;

procedure TForm1.Button1Click(Sender: TObject);
var
  Intent: JIntent;
  Calendar: JCalendar;
begin
  Calendar := TJCalendar.JavaClass.getInstance;
  Intent := TJIntent.Create;
  Intent.setType(StringToJString('vnd.android.cursor.item/event'));
  intent.putExtra(StringToJString('beginTime'), Calendar.getTimeInMillis());
  intent.putExtra(StringToJString('allDay'), true);
  intent.putExtra(StringToJString('rrule'), StringToJString('FREQ=YEARLY'));
  intent.putExtra(StringToJString('endTime'), Calendar.getTimeInMillis()+3600*1000);
  intent.putExtra(StringToJString('title'), StringToJString('Hello from Delphi'));
  SharedActivity.startActivity(Intent);
end;

在XE5中，他们从PlatformServices开始，并将Pickers Service放入其中：http://docwiki.embarcadero.com/Libraries/XE5/en/FMX.Pickers.IFMXPickerService
这段代码可能对你有用：

var
      PickerService: IFMXPickerService;
    begin
       if PlatformServices.Current.SupportsPlatformService(
           IFMXPickerService, Interface(PickerService))
    then
        FDateTimePicker := PickerService.CreateDateTimePicker;
        ...   // or
        FListPicker := PickerService.CreateListPicker;