[darkamerico]

Buscando halle este articulo: http://stackoverflow.com/questions/2...e-using-idhttp

Usando esa info modifique mi código y Funcionó:

Código Delphi [-]
procedure TfrmMain.btnUploadClick(Sender: TObject);
var
  PostData: TIdMultipartFormDataStream;
begin
  PostData := TIdMultipartFormDataStream.Create;
  try
    if open.Execute then
    begin
      PostData.AddFile('file', open.FileName);
      PostData.AddFormField('idFacultad',IntToStr(idFacultadSelected));
      IdHTTP1.Get('http://localhost/dasi/upload.php', TStream(nil));
      txtResp.Text:=idhttp1.Post('http://localhost/dasi/upload.php', PostData);
    end;
  finally
  begin
    ShowMessage('Documento Subido!');
    PostData.Free;
  end;
  end;
end;

Espero que les sea de utilidad

Saludos