We have performed an ab initio molecular dynamics simulation of the rotational dynamics of NH4+ ion in water. This work was motivated by the experimental evidence that the solvated NH4+ rotates rather fast, despite the expected formation of strong hydrogen bonds with water. We find that NH4+ is on average coordinated with five water molecules. Four water molecules form a long-lived tetrahedral cage around the ion, each molecule being hydrogen-bonded with one proton of NH4+. The fifth water molecule is much more mobile and occasionally exchanges with one of the four molecules in the tetrahedral cage. The hydrogen bonding of NH4+ with water is strong enough to prevent the free rotation of the ion, which instead tumbles in a sequence of discontinuous rotational jumps associated with the exchange of two water molecules in the tetrahedral cage. The simulated rotational dynamics is consistent with nuclear magnetic resonance data and encourages the use of ab initio simulations to describe the solvation of ions in water.