  We investigate the twist-angle and gate dependence of the proximity exchange
coupling in twisted graphene on monolayer Cr$_2$Ge$_2$Te$_6$ from first
principles. The proximitized Dirac band dispersions of graphene are fitted to a
model Hamiltonian, yielding effective sublattice-resolved proximity-induced
exchange parameters ($\lambda_{\textrm{ex}}^\textrm{A}$ and
$\lambda_{\textrm{ex}}^\textrm{B}$) for a series of twist angles between
0$^{\circ}$ and 30$^{\circ}$. For aligned layers (0$^{\circ}$ twist angle), the
exchange coupling of graphene is the same on both sublattices,
$\lambda_{\textrm{ex}}^\textrm{A} \approx \lambda_{\textrm{ex}}^\textrm{B}
\approx 4$ meV, while the coupling is reversed at 30$^{\circ}$ (with
$\lambda_{\textrm{ex}}^\textrm{A} \approx \lambda_{\textrm{ex}}^\textrm{B}
\approx -4$ meV). Remarkably, at 19.1$^{\circ}$ the induced exchange coupling
becomes antiferromagnetic: $\lambda_{\textrm{ex}}^\textrm{A} < 0,
\lambda_{\textrm{ex}}^\textrm{B} > 0$. Further tuning is provided by a
transverse electric field and the interlayer distance. The predicted proximity
magnetization reversal and emergence of an antiferromagnetic Dirac dispersion
make twisted graphene/Cr$_2$Ge$_2$Te$_6$ bilayers a versatile platform for
realizing topological phases and for spintronics applications.
