Can tick bites be treated with penicillin?

Not exactly: Various infections may be spread following tick bites - the most common is lyme disease. Amoxicillin (not penicillin) is approved for treating confirmed cases of lyme disease when clinical disease is present. For a tick bite in areas with high amounts of lyme disease it is useful to take a single dose of Doxycycline within 3 days to prevent lyme. Amoxicillin is not approved for prevention.

Yes: Amoxicillin is an alternative treatment. Doxycycline would be better.