  We perform the first suite of fully general relativistic magnetohydrodynamic
simulations of spinning massive black hole binary mergers. We consider binary
black holes with spins of different magnitudes aligned to the orbital angular
momentum, which are immersed in a hot, magnetized gas cloud. We investigate the
effect of the spin and degree of magnetization (defined through the fluid
parameter $\beta^{-1}\equiv p_{\mathrm{mag}}/p_{\mathrm{fluid}}$) on the
properties of the accretion flow. We find that magnetized accretion flows are
characterized by more turbulent dynamics, as the magnetic field lines are
twisted and compressed during the late inspiral. Post-merger, the polar regions
around the spin axis of the remnant Kerr black hole are magnetically dominated,
and the magnetic field strength is increased by a factor $\sim$10$^2$
(independently from the initial value of $\beta^{-1}$). The magnetized gas in
the equatorial plane acquires higher angular momentum, and settles in a thin
circular structure around the black hole. We find that mass accretion rates of
magnetized configurations are generally smaller than in the unmagnetized cases
by up to a factor $\sim$3. Black hole spins have also a suppressing effect on
the accretion rate, as large as $\sim$48\%. As a potential driver for
electromagnetic emission we follow the evolution of the Poynting luminosity,
which increases after merger up to a factor $\sim2$ with increasing spin,
regardless of the initial level of magnetization of the fluid. Our results
stress the importance of taking into account both spins and magnetic fields
when studying accretion processes onto merging massive black holes.
