  The effect of a random magnetic field in the convective zone of the Sun on
resonant neutrino spin oscillations, i.e. transitions of the type
$\nu_{eL}\to\tilde\nu_{\mu R}$, is considered. The average survival probability
and the expected experimental signals in the existing solar neutrino
experiments are computed as a function of the level of the noise and magnitude
of a constant magnetic field in the convective zone. From comparison with
observed detection rates we conclude that the RSFP solutions to the SNP with
negligible mixing angle are stable under the presence of low or moderate levels
of noise. Detection rates, specially in the Homestake experiment, are however
sensitive to large levels of noise. As a consequence, an upper limit on small
scale magnetic fluctuations is obtained from the combined solar data:
$\surd\langle B^2\rangle< 140-200 $ kG for the scale $L_0\sim 1000 $ km and
transition moment $\mu=10^{-11} \mu_B$.
