方法1
procedure TForm2.Button1Click(Sender: TObject);

var

  Pt: TPoint;

begin

  GetCursorPos(Pt);

  PopupMenu1.Popup(Pt.X, Pt.Y);

end;

方法2

设置控件的DropDownMenu 为右键单击（可手动设置） 这个功能只对ToolBar的 Button有效

PopMenu为右键单击

procedure TForm1.Button1Click(Sender: TObject);

begin

  ToolButton1.DropdownMenu := PopupMenu1;

end;