The Northern Irishman started dating the world number one tennis player this summer.
She tweeted a picture of the club and McIlroy replied: "Where's my racket?" before she responded with: "Your RACQUETS are on the way;)"
McIlroy, 22, has said that they spur on each other as he aspires to emulate her status as the world number one while Wozniacki, who has yet to win a tennis Grand Slam, wishes to win the US Open like McIlroy did in June.
"I want to become the best player in the world. I think we definitely spur each other on. She's number one in the world and I've got a major and we sort of both want what each other have," McIlroy said.
"She's got a great work ethic and it's something I can probably learn a lot from."
McIlroy is currently taking part in the Dunhill Links Championship, which takes place at three different courses over four days in Scotland.