  Extragalactic plasma jets are some of the few astrophysical environments able
to confine ultra-high-energy cosmic rays, but whether they are capable of
accelerating these particles is unknown. In this work, we revisit particle
acceleration at relativistic magnetized shocks beyond the local uniform field
approximation, by considering the global transverse structure of the jet. Using
large two-dimensional particle-in-cell simulations of a relativistic
electron-ion plasma jet, we show that the termination shock forming at the
interface with the ambient medium accelerates particles up to the confinement
limit. The radial structure of the jet magnetic field leads to a relativistic
velocity shear that excites a von K\'arm\'an vortex street in the downstream
medium trailing behind an over-pressured bubble filled with cosmic rays.
Particles are efficiently accelerated at each crossing of the shear flow
boundary layers. These findings support the idea that extragalactic plasma jets
may be capable of producing ultra-high-energy cosmic rays. This extreme
particle acceleration mechanism may also apply to microquasar jets.
