The Zeeman-induced shifts and splittings of low-J lines in the P-O(12) branch of the (0,0) band of the A(2)Pi(1/2)- X-2 Sigma(+) electronic transition of a cold molecular beam sample of ytterbium monofluoride, YbF, have been recorded. The Zeeman spectra for the (YbF)-Yb-171, (YbF)-Yb-172, and (YbF)-Yb-174 isotopologues have been analyzed using a standard effective Hamiltonian approach. The magnetic g-factors determined for the A(2)Pi(1/2)(nu = 0) state are rationalized using the predicted and observed electronic state distribution. The observed Zeeman tuning of the levels in the A(2)Pi(1/2) (nu = 0) state is unexpectedly large; this is caused by mixing with the B-2 Sigma(+) state.