The regular hexagon has rotational symmetry for angles of \(60^\circ\), \(120^\circ\), \(180^\circ\), \(240^\circ\), and \(300^\circ\) in addition to \(360^\circ\). Among these, the largest degree of rotation, excluding \(360^\circ\), that would turn a regular hexagon onto itself is \(300^\circ\).
So, the answer is \(300^\circ\).