  We present a phenomenological and numerical study of strong Alfv\'enic
turbulence in a magnetically dominated collisionless relativistic plasma with a
strong background magnetic field. In contrast with the non-relativistic case,
the energy in such turbulence is contained in magnetic and electric
fluctuations. We argue that such turbulence is analogous to turbulence in a
strongly magnetized non-relativistic plasma in the regime of broken
quasi-neutrality. Our 2D particle-in-cell numerical simulations of turbulence
in a relativistic pair plasma find that the spectrum of the total energy has
the scaling $k^{-3/2}$, while the difference between the magnetic and electric
energies, the so-called residual energy, has the scaling $k^{-2.4}$. The
electric and magnetic fluctuations at scale $\ell$ exhibit dynamic alignment
with the alignment-angle scaling close to $\cos\phi_\ell\propto \ell^{1/4}$. At
scales smaller than the (relativistic) plasma inertial scale, the energy
spectrum of relativistic inertial Alfv\'en turbulence steepens to $k^{-3.5}$.
