Virginia “Ginni” Rometty, the first female CEO of IBM (NYSE:IBM), plans to attend the Masters Tournament at the all-male Augusta National Golf Club. The tournament, one of golf’s most distinguished events, has been at the center of recent controversy because of Augusta National’s antiquated men-only membership policy.

The Masters has been held at Augusta National since its inception in 1940, but this year, scrutiny over the club’s refusal to extend membership to women has intensified because of Rometty’s position with IBM.

IBM — along with Exxon Mobil (NYSE:XOM) and AT&T (NYSE:T) — is a longtime sponsor of the event. Because of that sponsorship, Augusta has a tradition of extending membership invitations to the companies’ CEOs. So far, Rometty has not been invited to don the club’s iconic green blazer.

However, since she can attend as a guest, the Wall Street Journal has reported that Rometty, 54, is expected to be at the tournament to entertain clients. The CEO, who has led IBM since the beginning of the year, has kept mum on the matter.

Not keeping quiet on the issue are President Barack Obama and GOP presidential candidate Mitt Romney. Romney weighed in on the controversy yesterday with a public statement.

“I’m not a member of Augusta. I don’t know that I would qualify — my golf game is not that good — but certainly if I were a member and if I could run Augusta … of course I’d have women in Augusta,” Romney said at a campaign event in Pennsylvania.

Speaking to reporters on behalf of President Obama, White House press secretary Jay Carney said the president believes Augusta National should admit women.