  We perform the renormalization group improved collinear resummation of the
photon-gluon impact factors. We construct the resummed cross section for
virtual photon-photon ($\gamma^*\gamma^*$) scattering which incorporates the
impact factors and BFKL gluon Green's function up to the next-to-leading
logarithmic accuracy in energy. The impact factors include important
kinematical effects which are responsible for the most singular poles in Mellin
space at next-to-leading order. Further conditions on the resummed cross
section are obtained by requiring the consistency with the collinear limits.
Our analysis is consistent with previous impact factor calculations at NLO,
apart from a new term proportional to $C_F$ that we find for the longitudinal
polarization. Finally, we use the resummed cross section to compare with the
LEP data on the $\gamma^*\gamma^*$ cross section and with previous
calculations. The resummed result is lower than the leading logarithmic
approximation but higher than the pure next-to-leading one, and is consistent
with the experimental data.
