  The explicit expression for the probability of absorption of a twisted photon
by an atomic nucleus has been obtained. It is shown that photoabsorption obeys
the selection rule $j\geqslant|m_\gamma|$, where $j$ is the multipolarity of
the nuclear transition, when the nuclei lie near the axis along which a twisted
photon with a projection of the total angular momentum $m_\gamma$ propagates.
In the long-wave limit, the main contribution to the probability of absorption
of a twisted photon comes from the multipole transition with $j=|m_\gamma|$.
The absorption coefficient for twisted photons in a target consisting of many
nuclei has been found.
