  We treat RR flux backgrounds of type II string theory in the framework of
closed superstring field theory based on the NSR formalism, focusing on two
examples: (1) the pp-wave background supported by 5-form flux, and (2)
$AdS_3\times S^3\times M_4$ supported by mixed 3-form fluxes. In both cases, we
analyze the classical string field solution perturbatively, and compute the
correction to the dispersion relation of string states to quadratic order in
the RR flux. In the first example, our result is in a delicate way consistent
with that obtained from lightcone quantization of the Green-Schwarz string. In
the second example, we will obtain numerically the mass corrections to
pulsating type IIB strings in $AdS_3\times S^3\times M_4$. Our results, valid
at finite $AdS$ radius, agree with previously known answers in the
semiclassical limit and in the BMN limit respectively.
