Lingle, 58, is campaigning for the seat held the past 20 years by Sen. Daniel Akaka, an 87-year-old Democrat who is not seeking another term.
"If elected, first, foremost and always, my decisions will put Hawaii people first as we decide the critical issues facing our state and country," Honolulu's KHON-TV quoted Lingle as saying in her announcement.
She also paid tribute to Akaka.
"He always treated me with aloha even though we belonged to different political parties," she said. "Senator Akaka embodied the spirit of Aloha in Washington, D.C., and served the people of Hawaii with grace and dignity for 34 years."
The Democratic field includes U.S. Rep. Mazie Hirono and former Congressman Ed Case.
A poll in May showed Hirono holding a 22-point edge over Lingle, while Case led by 18, The Washington Post reported. Case's campaign issued a more recent poll that gave him a 10-point lead over Lingle with Hirono behind her by 5 percentage points. The Post said that poll drew criticism from national Democratic Party officials who questioned its reliability.