  We numerically calculate the optical conductivity of twisted graphene
bilayers within the continuum model. To obtain the imaginary part, we employ
the regularized Kramers-Kronig relation allowing us to discuss arbitrary twist
angles, chemical potential and temperature. We find that the Drude weight $D$
as function of the chemical potential $\mu$ closely follows the shell structure
of twisted bilayer displayed by the density of states. For certain angles, this
results in a transport gap D=0 at finite $\mu$. We also discuss the loss
function which, for low doping, is characterized by acoustic interband
"plasmons" and transitions close to the van Hove singularities. For larger
doping, the plasmon mode of decoupled graphene bilayer is recovered that is
damped especially for small wave numbers.
