Propagating individual cosmic rays in synthetic three-dimensional Kolmogorov turbulence, we calculate their anisotropy at the location of an observer. These are the first calculations of the cosmic ray anisotropy down to TeV energies for values of the turbulence coherence length that are realistic for the interstellar medium. We calculate the power spectrum 𝐶𝑙, of the cosmic ray anisotropy for different observer locations, and compare with observations. We also decompose the anisotropy onto spherical harmonics, and show that an important distinction should be made between higher order multipoles that are aligned with the local direction of the magnetic field at the observer’s location, and those that are not.