  Rotational misalignment or twisting of two mono-layers of graphene strongly
influences its electronic properties. Structurally, twisting leads to large
periodic supercell structures, which in turn can support intriguing strongly
correlated behaviour. Here, we propose a highly tunable scheme to synthetically
emulate twisted bilayer systems with ultracold atoms trapped in an optical
lattice. In our scheme, neither a physical bilayer nor twist is directly
realized. Instead, two synthetic layers are produced exploiting
coherently-coupled internal atomic states, and a supercell structure is
generated \emph{via} a spatially-dependent Raman coupling. To illustrate this
concept, we focus on a synthetic square bilayer lattice and show that it leads
to tunable quasi-flatbands and Dirac cone spectra under certain magic supercell
periodicities. The appearance of these features are explained using a
perturbative analysis. Our proposal can be implemented using available
state-of-the-art experimental techniques, and opens the route towards the
controlled study of strongly-correlated flat band accompanied by hybridization
physics akin to magic angle bilayer graphene in cold atom quantum simulators.
