  The magnetic field strength in molecular clouds is a fundamental quantity for
theories of star formation. It is estimated by Zeeman splitting measurements in
a few dense molecular cores, but its volume--averaged value within large
molecular clouds (over several parsecs) is still uncertain. In this work we
provide a new method to constrain the average magnetic field strength in
molecular clouds. We compare the power spectrum of gas density of molecular
clouds with that of two $350^3$ numerical simulations of supersonic MHD
turbulence. The numerical simulation with approximate equipartition of kinetic
and magnetic energies (model A) yields the column density power spectrum
$P(k)\propto k^{-2.25\pm 0.01}$, the super--Alfv\'{e}nic simulation (model B)
$P(k)\propto k^{-2.71\pm 0.01}$. The column density power spectrum of the
Perseus, Taurus and Rosetta molecular cloud complexes is found to be well
approximated by a power law, $P_{\rm o}(k)\propto k^{-a}$, with $a=2.74\pm
0.07$, $2.74\pm 0.08$ and $2.76\pm 0.08$ respectively. We conclude that the
observations are consistent with the presence of super--Alfv\'{e}nic turbulence
in molecular clouds (model B) while model A is inconsistent (more than 99%
confidence) with the observations.
