  We study the impact of active galactic nuclei (AGN) on the CO Spectral Line
Energy Distribution (SLED) of high-$z$ galaxies. In particular, we want to
assess if the CO SLED can be used as a probe of AGN activity. To this purpose,
we develop a semi-analytical model that takes into account the radiative
transfer and the clumpy structure of giant molecular clouds where the CO lines
are excited, their distribution in the galaxy disk, and the torus obscuration
of the AGN radiation. We study the joint effect on the CO SLED excitation of
(i) the X-ray luminosity from the AGN ($L_{X}$), (ii) the size of the molecular
disk, (iii) the inclination angle ($\Omega$) of the torus with respect to the
molecular disk, and (iv) the GMC mean density. We also discuss the possibility
of an enhanced Cosmic Ray Ionization Rate (CRIR). We find that the X-ray
Dominated Region (XDR) generated by the AGN in every case enhances the CO SLED
for $J>5$, with increasing excitation of high-$J$ CO lines for increasing X-ray
luminosity. Because high-$z$ galaxies are compact, the XDR region typically
encloses the whole disk, thus its effect can be more important with respect to
lower redshift objects. The impact of the XDR can be disentangled from an
enhanced CRIR either if $L_X>10^{44} \rm \,erg\, s^{-1}$, or if $\Omega \geq
60^{\circ}$. We finally provide predictions on the CO(7-6)/[CII] and
CO(17-16)/[CII] ratios as a function of $L_X$, which can be relevant for ALMA
follow up of galaxies and quasars previously detected in [CII].
