  The rotational dynamics of the water molecule includes tumbling, vibration,
libration, collisions and the breaking and reforming of hydrogen bonds. A
probability density function describing the angular evolution of a fixed-length
atom-atom vector as a L\'{e}vy rotor is derived containing just two dynamical
parameters: the L\'{e}vy parameter $\alpha$ and a rotational time constant
$\tau$. A L\'{e}vy parameter $\alpha\!<\!2$ signals anomalous (non-Brownian)
motion. A molecular dynamics (MD) simulation of water at 298\,K validates the
probability density function for the intra-molecular $^1$H--$^1$H dynamics of
water. The rotational dynamics of water is found to be approximately Brownian
at sub-picosecond time intervals but becomes increasingly anomalous at longer
times due to hydrogen-bond breaking and reforming. The L\'{e}vy parameter
$\alpha$ drops to 0.82 with the rotational time parameter in the range $8 \! <
\! \tau \! < \! 11$\,ps. The L\'{e}vy rotor model is used to estimate the
intra-molecular contribution to the longitudinal nuclear-magnetic-resonance
relaxation rate $R_{1,{\rm intra}}$ due to dipolar $^1$H--$^1$H interactions.
It is found that $R_{1,{\rm intra}}$ contributes $63\,\pm 3$\% to the overall
relaxation rate of water at room temperature.
