Countries that have been opening to vaccinated Americans are accepting CDC vaccine cards as ‘proof’ of vaccination. These are pieces of cardstock you can print off the internet, and real ones are often filled out by hand. There is no central federal database of who has had a vaccine, those specifics are generally held at the state level – and the quality of recordkeeping varies dramatically.
The Secretary of Homeland Security says vaccine passports are under serious consideration as a way of helping Americans meet the requirements of entry for foreign countries.