Fuld said the giveaway will be the first in his honor.
"I was maybe close to getting an Iowa Cub T-shirt giveaway, but I didn't even make the cut there," said Fuld, who came to the Rays in a trade that sent Matt Garza to the Cubs.
Fuld leads the American League in stolen bases, and on Monday night, the native of Durham, N.H., made his Fenway Park debut in grand style with four hits, including a home run, triple and two doubles. He is just the fourth New Hampshire born player to homer at Fenway, the first since Boston's Phil Plantier on Oct. 3, 1992, against the Yankees.
Manager Joe Maddon has enjoyed watching the Stanford-educated Fuld become a sensation. Fuld's father, Kenneth, is dean of the college of liberal arts at the University of New Hampshire, while his mother, Amanda Merrill, is a New Hampshire state senator.
"It's been fun to watch," Maddon said. "Just getting to know him, conversationally, and watching him play, the fact that he comes from such an educated background makes it even more interesting, I think. I met his dad, [but] I did not realize [he was a dean]. He's a very nice man. I have not met his mom yet. He's got an unusual background for a Major League Baseball player, and I really enjoy that and that he is that good.
"I've talked about it with a lot of our guys. Sometimes guys just need opportunities, and we've been able to give players opportunities over the last couple of years who have done pretty well for themselves, and I think he's just the next in line."
Fuld grew up a huge Red Sox fan, attending many games as a youth. So playing at Fenway Park this week proved to be dreamland for the 29-year-old.
"I think just that first moment of stepping onto the field in that first inning, I'll never forget that," Fuld said. "The home run was pretty amazing, too. That's going to be hard to forget. That's probably what's going to stand out the most. After that, I was just giddy and everything after that was just icing on the cake. There are so many memories to take away from these two days. It feels like two weeks to me."