  We present a set of three-dimensional, global, general relativistic radiation
magnetohydrodynamic simulations of thin, radiation-pressure-dominated accretion
disks surrounding a non-rotating, stellar-mass black hole. The simulations are
initialized using the Shakura-Sunyaev model with a mass accretion rate of
$\dot{M} = 3 L_\mathrm{Edd}/c^2$ (corresponding to $L=0.17 L_\mathrm{Edd}$).
Our previous work demonstrated that such disks are thermally unstable when
accretion is driven by an $\alpha$-viscosity. In the present work, we test the
hypothesis that strong magnetic fields can both drive accretion through the
magneto-rotational instability and restore stability to such disks. We test
four initial magnetic field configurations: 1) a zero-net-flux case with a
single, radially extended set of magnetic field loops (dipole); 2) a
zero-net-flux case with two radially extended sets of magnetic field loops of
opposite polarity stacked vertically (quadrupole); 3) a zero-net-flux case with
multiple radially concentric rings of alternating polarity (multi-loop); and 4)
a net-flux, vertical magnetic field configuration (vertical). In all cases, the
fields are initially weak, with the gas-to-magnetic pressure ratio $\gtrsim
100$. Based on the results of these simulations, we find that the dipole and
multi-loop configurations remain thermally unstable like their
$\alpha$-viscosity counterpart, in our case collapsing vertically on the local
thermal timescale and never fully recovering. The vertical case, on the other
hand, stabilizes and remains so for the duration of our tests (many thermal
timescales). The quadrupole case is intermediate, showing signs of both
stability and instability. The key stabilizing criteria is, $P_\mathrm{mag}
\gtrsim 0.5P_\mathrm{tot}$ with strong toroidal fields near the disk midplane.
We also report a comparison of our models to the standard Shakura-Sunyaev disk.
