  High energy positrons can be efficiently created through high-energy photons
splitting into electron-positron pairs under the influence of the Coulomb
field. Here we show that a new degree of freedom-the intrinsic orbital angular
momentum (OAM) can be introduced into relativistic positrons when the incident
photons are twisted. We developed the full-twisted scattering theory to
describe the transfer of angular momentum before and after the interaction. It
is found that the total angular momentum (TAM) of the photon is equally
distributed among the positron and electron. For each photon TAM value, the
generated leptons gain higher average OAM number when the photon spin is
anti-parallel to its TAM. The impact of photon polarization on the OAM spectrum
profile and the scattering probability is more significant at small photon TAM
numbers, owing to the various interaction channels influenced by flipping the
photon spin. Our work provides the theoretical basis to study OAM physics in
particle scattering and to obtain copious relativistic vortex positrons through
the Beth-Heitler process.
