It is a classical question that of classifying smooth nondegenerate projective varieties \(X \subset \mathbb{P}^N\) of degree \(d\) and codimension \(e\) not cut out by hypersurfaces of degree smaller than or equal to \(d-e+1\) (on an algebraically closed field of characteristic zero). In this context, projected Roth varieties -- a particular set of divisors on some rational scrolls (see Def. 0.1) -- appear as an important set of varieties with this property. Therefore it seems of interest to compute their Castelnuovo-Mumford regularity. The main result of this paper (see Thm. 0.4) is a study of the \(m\)-regularity for non linearly normal projected Roth varieties in terms of two invariants \((a, \mu)\) which determines completely, by construction, the Roth variety. This result is applied to the question of the degree of the equations defining these varieties (see Cor. 0.5 and and improvement in Cor 0.6, under some extra hypotheses).