Spin-orbit scattering suppresses Zeeman splitting of individual energy levels in small metal particles. This suppression becomes significant when the spin-orbit scattering rate τ-1so is comparable to the quantum level spacing δ. At small δτso the g-factor exhibits strong mesoscopic fluctuations. We find the shape of their distribution function using the random matrix theory, and express its parameters in terms of physical characteristics: τso, δ, the electron mean free path l, and the particle size L. At δτso-->0 the average g-factor levels off at a small value g~\(l/L\)1/2. However, in 2D quantum dots the g-factor is strongly enhanced by spin-orbit coupling.