  We propose to study cosmic reionization using absorption line spectra of
high-redshift Gamma Ray Burst (GRB) afterglows. We show that the statistics of
the dark portions (gaps) in GRB absorption spectra represent exquisite tools to
discriminate among different reionization models. We then compute the
probability to find the largest gap in a given width range [Wmax, Wmax + dW] at
a flux threshold Fth for burst afterglows at redshifts 6.3 < z < 6.7. We show
that different reionization scenarios populate the (Wmax, Fth) plane in a very
different way, allowing to distinguish among different reionization histories.
We provide here useful plots that allow a very simple and direct comparison
between observations and model results. Finally, we apply our methods to GRB
050904 detected at z = 6.29. We show that the observation of this burst
strongly favors reionization models which predict a highly ionized
intergalactic medium at z~6, with an estimated mean neutral hydrogen fraction
xHI = 6.4 \pm 0.3 \times 10^-5 along the line of sight towards GRB 050904.
