When travelling to the US you have to complete a US Attestation Form. Authorities may not always ask to see it but you still need to complete it.

The form states that you are fully vaccinated against COVID. The link to the US Attestation form can be found here: 

Proof-of-COVID-19-Vaccination-For-Noncitizen-Nonimmigrants-Passenger-Disclosure-and-Attestation PDF Document · 259 KB

This version is supposed to expire at the end of this year. So look out for an updated version. Remember the form must be completed prior to departure to the US. Many airlines offer a facility to upload directly through their website. 

Happy US travels.