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Having a blood drive at a convention is a tradition that started with the science fiction community, specifically by Robert Heinlein and his fans, in the 1960s and is continued today.
Many Star Trek fan clubs, and to a smaller extent, other fandoms, sponsor The Red Cross at local conventions as a community service/charity.
While a fixture at science fiction cons, the first blood drive hosted at a Star Trek-focused convention was in January 1977 at PSST Con.In 1981, a fan in the UK asked:
I have just read David Gerrold's column in January's Starlog, in which he mentions a blood-drive, where fans give blood. Wouldn't it be a lovely gesture if a similar set-up could be arranged at British cons? Would it be possible to have the mobile Blood Transfusion Unit set up in the car park of our con hotel for a day?. I'm sure there would be enough people willing to donate their blood and it would show people that we are prepared to help contribute towards the future of others. I for one feel that although STAR TREK has a message worth listening to, we fans seldom do anything to show we actually care about that message. Granted, we donate to charities but, by giving blood, we could help a far greater number of people. 
- from STAG #46