Facebook introduced the feature in May, enabling people to state their wishes to become donors in an attempt to reduce the long waiting lists for organs and tissue, The Hastings Center in New York said.
"By the end of the day of the announcement, 6,000 people had enrolled through 22 state registries," Hastings officials wrote on the organization's Bioethics Forum blog.
In California alone, they said, 3,900 people signed up, compared with 70 on a typical day.
After two weeks the rate of registration returned to previous levels, they said, but suggested strategies for using the full potential of social media to achieve a sustained increase in registration.
"State registries could include social sharing on their sites, so that once a person joins the registry, he or she has the option to share this information via Facebook, Twitter, and other social networks which should drive awareness among friends and family," Hastings officials wrote.
Social media companies could allow donor registries to advertise at no cost, they suggested.
"Facebook has challenged other technology companies to show corporate leadership and has demonstrated the power of social media to encourage altruism," they said.