We present a procedure to constrain the redshifts of obscured ($N_H > 10^{22}$ cm$^{-2}$) Active Galactic Nuclei (AGN) based on low-count statistics X-ray spectra, which can be adopted when photometric and/or spectroscopic redshifts are unavailable or difficult to obtain. We selected a sample of 54 obscured AGN candidates on the basis of their X-ray hardness ratio, $HR>-0.1$, in the Chandra deep field ($sim$479 ks, 335 arcmin$^2$) around the $z=6.3$ QSO SDSS J1030+0524. The sample has a median value of $approx80$ net counts in the 0.5-7 keV energy band. We estimate reliable X-ray redshift solutions taking advantage of the main features in obscured AGN spectra, like the Fe 6.4 keV K$mathrm{alpha}$ emission line, the 7.1 keV Fe absorption edge and the photoelectric absorption cut-off. The significance of such features is investigated through spectral simulations, and the derived X-ray redshift solutions are then compared with photometric redshifts. Both photometric and X-ray redshifts are derived for 33 sources. When multiple solutions are derived by any method, we find that combining the redshift solutions of the two techniques improves the rms by a factor of two. Using our redshift estimates ($0.1lesssim z lesssim 4$), we derived absorbing column densities in the range $sim 10^{22}-10^{24}$ cm$^{-2}$ and absorption-corrected, 2-10 keV rest-frame luminosities between $sim 10^{42}$ and $10^{45}$ erg s$^{-1}$, with median values of $N_H = 1.7 times 10^{23}$ cm$^{-2}$ and $L_{mathrm{2-10, keV}} = 8.3times10^{43}$ erg s$^{-1}$, respectively. Our results suggest that the adopted procedure can be applied to current and future X-ray surveys, for sources detected only in the X-rays or that have uncertain photometric or single-line spectroscopic redshifts.
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