Does Delta airline charge international passengers for baggage?

The first bag is free when traveling with Delta internationally. Whether you get a 2nd bag for free or not depends on what countries you are flying to and from. It also depends on whether you are a medallion or flying in a premium cabin. Delta American Express Cards do not get you a 2nd bag on international flights. Those cards only affect US domestic flights. All the rules are on Delta's website at the related link.