What would you be willing to give for an ultraexclusive T-shirt? Hundreds of dollars? Hours spent waiting in line?

How about blood?

A white graphic T-shirt featuring the “Peanuts” character Snoopy has become an object of obsession online. The shirt was dropped by the Red Cross and “Peanuts” as part of a promotion to encourage blood donation in April. It is free — though the only way to get it is by donating blood, plasma or platelets.

The prize shirt shows Snoopy, in the guise of his alter ego, Joe Cool, leaning nonchalantly against the distinctive Red Cross emblem above a caption that reads: “Be cool. Give blood.”

A video posted Wednesday on TikTok about donating blood specifically to get the Snoopy shirt was viewed more than four million times. Dozens of similar clips followed, some of them set to the Vince Guaraldi Trio’s jazzy instrumental “Linus and Lucy.”

“They’re finally realizing we will do anything for merch,” one commenter wrote.

Mollie Fox, a senior at Belmont University in Nashville, was one of the recent donors motivated at least in part by the prospect of the Snoopy shirt. At her appointment on Wednesday, she said she tried to play it as cool as the famous beagle.

“I was at a little cubicle where they took my hemoglobin levels and the guy was like: ‘Oh, by the way, we’re doing a promotion where we’re giving out Snoopy T-shirts for donors. Do you want one?’” Ms. Fox said. “I played it off pretending I didn’t know. Like, ‘Yeah, sure.’”

She was also following the example of her father, a frequent blood donor, she added. “He’s like, in the hall of fame in our hometown blood bank,” Ms. Fox said.

The experience was easy, she added. (Donating blood is generally low risk for those eligible.) She left the appointment with the T-shirt, several free packets of Cheez-Its and an appointment to donate blood again in June.

The Red Cross has offered tie-in merchandise at previous blood drives. In 2019, the nonprofit organization teamed up with HBO for “Bleed for the Throne,” a campaign in which it offered T-shirts commemorating the final season of “Game of Thrones” and a chance to win a replica throne.

“The strategy is to introduce blood donation into fan bases to really inspire new donors through the lens of their existing interests and their passion points,” said Darren Irby, the Red Cross’s executive director of national brand partnerships.

To help the latest campaign gain traction, the organization paid a handful of influencers to post advertisements for the “Peanuts” partnership on TikTok and Instagram. The videos from everyday TikTok users are the ones really going viral, though.

Cristina Perez, a 20-year-old bioengineering student at the University of Pennsylvania, said she saw the T-shirt on TikTok on Wednesday night and swiftly booked an appointment for the next day.

“I was like, I need this shirt,” she said.

After giving blood for the first time, she said that she was considering doing it more often. And as weather warms, she plans to wear her Snoopy shirt “with some longer jorts, a casual look,” she said, using a portmanteau of “jean shorts.” She added that she hoped the Red Cross would release a SpongeBob shirt next.

Others on social media lamented that restrictions around blood donation would prevent them from getting the Snoopy shirt. The Food and Drug Administration has long excluded most gay and bisexual men from blood donation. In January, the agency said it would loosen those restrictions, instead screening donors depending on their recent sexual activity. One user wrote onscreen in a TikTok video that he was unable to donate blood because he recently had a boyfriend.

The American Red Cross created its civilian blood donation program in the 1940s. During the coronavirus pandemic, the organization said it experienced a “staggering” drop in its blood supply. Mr. Irby said young people often begin donating blood at high school or college blood drives, many of which were put on hold during the pandemic. He now sees many young people introduced to blood donation on social media instead.

Snoopy, the floppy-eared beagle from the comic strip by Charles M. Schulz, is no stranger to public adoration. In the strip and in more than 40 “Peanuts” television specials, he appeared as both Charlie Brown’s sidekick and an auteur of vivid fantasy personas, including Joe Cool.

Peyton Weber, 19, a student at Joliet Junior College in Illinois, said that the “Peanuts” character was a smart choice for a Red Cross tie-in, because of his appeal across generations. Mr. Weber, a longtime “Peanuts” fan, was especially excited that the T-shirt featured Joe Cool.

“It’s just Snoopy with sunglasses, but it’s a whole different thing,” he said. “What’s cooler than a dog with sunglasses?”

He added that he was hoping the Red Cross wouldn’t run out of the shirts before his Tuesday appointment. The promotion is scheduled to run through April 23. (“While supplies last,” Mr. Irby cautioned.)

In a recent video, a TikTok user posted a clip of what appeared to be paramedics assisting a blood donor who had apparently passed out during the process.

“Anything for the Snoopy shirt,” the onscreen caption said.