  The distribution of arrival directions of cosmic rays is remarkably
isotropic, which is a consequence of their repeated scattering in magnetic
fields. Yet, high-statistics observatories like IceCube and HAWC have revealed
the presence of small-scale structures at levels of 1 part in 10,000 at
hundreds of TeV, which are not expected in typical diffusion models of cosmic
rays. We follow up on the suggestion that these small-scale anisotropies are a
result of cosmic ray streaming in a particular realisation of the turbulent
magnetic field within a few scattering lengths in our local Galactic
neighbourhood. So far, this hypothesis has been investigated mostly
numerically, by tracking test particles through turbulent magnetic fields. For
the first time, we present an analytical computation that through a
perturbative approach allows predicting the angular power spectrum of cosmic
ray arrival directions for a given model of turbulence. We illustrate this
method for a simple, isotropic turbulence model and we find remarkable
agreement with the results of numerical studies.
