  We investigate a slowly rotating black hole solution in a novel
Einstein-Maxwell-scalar theory, which is prompted by the classification of
general Einstein-Maxwell-scalar theories. The gyromagnetic ratio of this black
hole is calculated, and it increases as the second free parameter $\beta$
increases, but decreases with the increasing parameter $\gamma\equiv \frac{2
\alpha^{2}}{1+\alpha^2}$. In the Einstein-Maxwell-dilaton (EMD) theory, the
parameter $\beta$ vanishes, but the free parameter $\alpha$ governing the
strength of the coupling between the dilaton and the Maxwell field remains. The
gyromagnetic ratio is always less than $2$, the well-known value for a
Kerr-Newman (KN) black hole as well as for a Dirac electron. Scalar hairs
reduce the magnetic dipole moment in dilaton theory, resulting in a drop in the
gyromagnetic ratio. However, we find that the gyromagnetic ratio of two can be
realized in this Einstein-Maxwell-scalar theory by increasing $\beta$ and the
charge-to-mass ratio $Q/M$ simultaneously (recall that the gyromagnetic ratio
of KN black holes is independent of $Q/M$). The same situation also applies to
the angular velocity of a locally non-rotating observer. Moreover, we analyze
the period correction for circular orbits in terms of charge-to-mass ratio, as
well as the correction of the radius of the innermost stable circular orbits.
It is found the correction increases with $\beta$ but decreases with $Q/M$.
Finally, the total radiative efficiency is investigated, and it can vanish once
the effect of rotation is considered.
