  The quark-gluon plasma produced in heavy-ion collisions is anisotropic
throughout its evolution. This anisotropy changes the physics of jet-medium
interaction, making it dependent on the momentum direction of the jet. In this
paper we analyze transverse momentum broadening of a jet parton interacting
with soft gluons in an anisotropic plasma. Our analysis equally applies to
momentum broadening of quasiparticles in kinetic theory. We subtract
contribution from instability modes in the deep infrared and discuss how our
calculation should be complemented in that regime. The resulting anisotropic
collision kernel for momentum broadening is qualitatively different from the
equilibrium collision kernel and from the isotropic ansatz used in effective
kinetic theory. Because of increased medium screening, there is substantially
less transverse broadening at low and intermediate momenta.
