Place the grid in editor mode, then get a handle to the edit box and send a EM_SETSEL message, passing the initial position where you want the cursor to appear, and the positon of the ending selection (if you wish to highlight text). The following example sets the cursor to the second character in the edit control, and does not select any text.

Example:
procedure TForm .Button Click(Sender: TObject);
var
  h : THandle;
begin
  Application.ProcessMessages;
  DbGrid .SetFocus;
  DbGrid .EditorMode := true;
  Application.ProcessMessages;
  h := Windows.GetFocus;
  SendMessage(h, EM_SETSEL, 2, 2);
end;