  The pairing symmetry of an effective Hamiltonian for interacting fermions on
a twisted bilayer graphene superlattice is studied with the determinant quantum
Monte Carlo method. The model has the symmetry of a triangle lattice and a
nearly-flat low energy band, features which underlie the magic-angle twisted
bilayer graphene superlattice. We show that the low temperature phase is
insulating at half-filling, even for relatively weak interactions. The natures
of the spin and pairing correlations upon doping are determined, and exhibit an
electron-hole asymmetry consistent with experiment. Among the pairing
symmetries allowed, we demonstrate that the dominating channels are $d$-wave,
opening the possibility of condensation into an unconventional
$d_{x^2-y^2}+id_{xy}$ phase, which is characterized by an integer topological
invariant and gapless edge states.
