  A new method to determine the spin tune is described and tested. In an ideal
planar magnetic ring, the spin tune - defined as the number of spin precessions
per turn - is given by $\nu_s = \gamma G$ (gamma is the Lorentz factor, $G$ the
magnetic anomaly). For 970 MeV/c deuterons coherently precessing with a
frequency of ~120 kHz in the Cooler Synchrotron COSY, the spin tune is deduced
from the up-down asymmetry of deuteron carbon scattering. In a time interval of
2.6 s, the spin tune was determined with a precision of the order $10^{-8}$,
and to $1 \cdot 10^{-10}$ for a continuous 100 s accelerator cycle. This
renders the presented method a new precision tool for accelerator physics:
controlling the spin motion of particles to high precision is mandatory, in
particular, for the measurement of electric dipole moments of charged particles
in a storage ring.
