To fully understand cosmic black hole growth we need to constrain the population of heavily obscured active galactic nuclei (AGN) at the peak of cosmic black hole growth ($zsim$1-3). Sources with obscuring column densities higher than $mathrm{10^{24}}$ atoms $mathrm{cm^{-2}}$, called Compton-thick (CT) AGN, can be identified by excess X-ray emission at $sim$20-30 keV, called the Compton hump. We apply the recently developed Spectral Curvature (SC) method to high-redshift AGN (2<z<5) detected with Chandra. This method parametrizes the characteristic Compton hump feature cosmologically redshifted into the X-ray band at observed energies <10 keV. We find good agreement in CT AGN found using the SC method and bright sources fit using their full spectrum with X-ray spectroscopy. In the Chandra deep field south, we measure a CT fraction of $mathrm{17^{+19}_{-11}%}$ (3/17) for sources with observed luminosity $mathrm{>5times 10^{43}}$ erg $mathrm{s^{-1}}$. In the Cosmological evolution survey (COSMOS), we find an observed CT fraction of $mathrm{15^{+4}_{-3}%}$ (40/272) or $mathrm{32pm11 %}$ when corrected for the survey sensitivity. When comparing to low redshift AGN with similar X-ray luminosities, our results imply the CT AGN fraction is consistent with having no redshift evolution. Finally, we provide SC equations that can be used to find high-redshift CT AGN (z>1) for current (XMM-Newton) and future (eROSITA and ATHENA) X-ray missions.
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