"In the U.S., 353 million doses have been given so far"[1] which covers 164 million people[2].

GP suggests that 12366 have died directly from the vaccine which would put it at 12366/164000000 or just above 0.0075%.

(Assuming those vaccine death numbers are just for the US otherwise the percentage drops even further...)

[1] https://www.bloomberg.com/graphics/covid-vaccine-tracker-glo... [2] https://www.scientificamerican.com/article/breakthrough-infe...