Aerobraking by itself (or is it aerocapture) probably wouldn't be nearly precise enough for that. To the best of my knowledge, no one has ever attempted to do a full aerocapture into orbit. Instead, they've fired thrusters to enter a highly elliptical orbit and then used aerobraking to eventually circularize. The goal would be to burn off (literally) the extra velocity so that the tug would be in orbit around the Earth. You can drop the apogee fairly quickly once you're in orbit by keeping the perigee low, say 140 kilometers or so.

The Earth has a much denser atmosphere than Mars, so it might be possible to do an initial aerocapture followed by circularization maneuvers that would put the vehicle into a position where it could rendevous with on-orbit facilities. I wouldn't recommend the ISS because it's inclination is too high, but it might be used simply because we've paid so much money for it even if it is in an inefficient orbit for lunar trips.