Upvote:3
Since the yellow vaccination book (which most travellers had in the 1960's) are filled out by qualified doctors, your doctor should be able to add an entry based on the Vaccination Record Card entry.
In Germany a International Certificate of Vaccination is common place and can be bought for β¬ 2 in most Apotheke.
This serves the same purpose as the US Vaccination Record Card.
My doctor simply fills it out for each vaccination.
Often the flu vaccination have a small sticker, which is placed in the book if you have it with you when getting the shot and stamped on the right hand side by the doctor (or on their behalf).
This may be true for the COVID-19 vaccine, since the image below shows 2 stickers being used.
Normally the stickers contain the brand name and a production number for each shot, so assume this image only shows what it could look like.

Update (2021-03-19):
I just received a reply from a friend in the US who ordered a CDC International Certificate of Vaccination, at the given link below, on the 7th of January 2021:
I received today, a package delivered by ups containing 25 of said yellow forms. I guess I will take them with me tomorrow when I get my 2nd shot.
They filled in the vaccination history.
Sources: