We study the dynamics of large polarons in diatomic molecular chains, at zero temperature, under the influence of an external, periodic in time, electric field of zero mean value. We show that in asymmetric chains, i.e. chains with two different atoms per unit cell, a harmonic unbiased field causes a drift of such polarons. Such a drift current, known as the ratchet phenomenon, depends strongly on the parameters of the chain; in particular, on the extent of the anisotropy of the chain and on the size of the polaron. Moreover, the drift takes place only if the intensity and the period of the field exceed some critical values which also depend on the parameters of the chain. We show that this directed current of polarons is a complicated phenomenon. It takes place in dissipative systems with a broken spatial symmetry and is generated by the interplay between the Peierls-Nabarro barrier and the impact of the external field on the charged polarons. The dependence of the amplitude of the polaron oscillations, the size of the drift per period of the external field and the average velocity are determined as a function of the intensity of the field and of its frequency.