Diffusion MRI classically uses linear gradients to encode information about micro-structure in the loss of signal magnitude. When replaced by gradients varying quadratically in space, anisotropic diffusion results in a net phase shift, while the signal magnitude is largely preserved. This allows the extraction of information from signal phase inaccessible to other diffusion MRI methods. The phase evolution of anisotropic fiber phantoms were studied in simulations and diffusion experiments. Simulations confirm increasing phase change with increasing anisotropy and mixing time between diffusion gradients. First MR experiments with different mixing times show a phase shift in good agreement with theoretical estimate.