  We theoretically study the optical activity in a doped system and derive the
optical activity tensor from a light wavevector-dependent linear optical
conductivity. Although the light-matter interaction is introduced through the
velocity gauge from a minimal coupling Hamiltonian, we find that the well-known
``false divergences'' problem can be avoided in practice if the electronic
states are described by a finite band effective Hamiltonian, such as a few-band
tight-binding model. The expression we obtain for the optical activity tensor
is in good numerical agreement with a recent theory derived for an undoped
topologically trivial gapped system. We apply our theory to the optical
activity of a gated twisted bilayer graphene, with a detailed discussion of the
dependence of the results on twist angle, chemical potential, gate voltage, and
location of rotation center forming the twisted bilayer graphene.
