We present a novel family of rotational-invariant measures for High Angular Resolution Diffusion Imaging (HARDI) data. This research is motivated by need for the developing new biomarkers and thereby facilitating population-based studies in HARDI. From a spherical harmonics (SH) representation of the angular information in diffusion MRI, we derive rotational-invariant measures computed as homogeneous polynomials of the SH coefficients. When the SH is truncated to order L=4, we find a total of 12 such invariants, which are expected to be sensitive to subtle changes in white matter structure, not captured by tensor fractional anisotropy (FA) or generalized fractional anisotropy (GFA). The method is generalizable to any spherical function, we report here the derivation and results based on the apparent diffusion coefficient (ADC) profile.