  From previous studies of the effect of primordial magnetic fields on early
structure formation, we know that the presence of primordial magnetic fields
during early structure formation could induce more perturbations at small
scales (at present 1-10 Mpc/h) as compared to the usual LCDM theory. Matter
power spectrum over these scales are effectively probed by cosmological
observables such as shear correlation and Ly-alpha clouds, In this paper we
discuss the implications of primordial magnetic fields on the distribution of
Ly-alpha clouds. We simulate the line of sight density fluctuation including
the contribution coming from the primordial magnetic fields. We compute the
evolution of Ly-alpha opacity for this case and compare our theoretical
estimates of Ly-alpha opacity with the existing data to constrain the
parameters of the primordial magnetic fields. We also discuss the case when the
two density fields are correlated. Our analysis yields an upper bounds of
roughly 0.3-0.6 nG on the magnetic field strength for a range of nearly scale
invariant models, corresponding to magnetic field power spectrum index n \simeq
-3.
