In graphene, charged defects break the electron-hole symmetry and can even
give rise to exotic collapse states when the defect charge exceeds a critical
value which is proportional to the Fermi velocity. In this work, we investigate
the electronic properties of twisted bilayer graphene (tBLG) with charged
defects using tight-binding calculations. Like monolayer graphene, tBLG
exhibits linear bands near the Fermi level but with a dramatically reduced
Fermi velocity near the magic angle (approximately 1.1{\deg}). This suggests
that the critical value of the defect charge in magic-angle tBLG should also be
very small. We find that charged defects give rise to significant changes in
the low-energy electronic structure of tBLG. Depending on the defect position
in the moir\'e unit cell, it is possible to open a band gap or to induce an
additional flattening of the low-energy valence and conduction bands. Our
calculations suggest that the collapse states of the two monolayers hybridize
in the twisted bilayer. However, their in-plane localization remains largely
unaffected by the presence of the additional twisted layer because of the
different length scales of the moir\'e lattice and the monolayer collapse state
wavefunctions. These predictions can be tested in scanning tunnelling
spectroscopy experiments.