In that case, never mind! 
Lynn Redgrave.
Since she didn’t become famous until she became PM of Israel, she fails the famous-before-naturalization test.
Svetlana Stalina Alliluyeva Peters.
From her obit in New York Times, Lana Peters, Stalin’s Daughter, Dies at 85, Nov. 28, 2011
[QUOTE=New York Times]
Information about the next few years is sketchier. Ms. Peters became a United States citizen in 1978 and later told The Trenton Times that she had registered as a Republican and donated $500 to the conservative magazine National Review, saying it was her favorite publication.
[/quote]
Among her many name changes throughout her life, she shortened her name from Svetlana to simply Lana. There’s a joke that she had to petition a court and argue before a judge to make this “official”. The judge’s ruling:
No Svet.
(Missed edit windor for above post.)
And yes, [del]Svet[/del]Lana was an international “celebrity” (of sorts) when she arrived in the United States, well before becoming a citizen. She arrived in 1967, at a fairly high-tension time during the Cold War, and denounced Stalin and the Soviet Union, creating an international stir. Some excerpts from the NYT article:
[QUOTE=New York Times]
Once in India, Ms. Alliluyeva, as she was known now, evaded Soviet agents in the K.G.B. and showed up at the United States Embassy in New Delhi seeking political asylum. The world watched in amazement as Stalin’s daughter, granted protection, became the most high-profile Soviet exile since the ballet virtuoso Rudolf Nureyev defected in 1961. The United States quickly dispatched a C.I.A. officer to help her travel through Italy to neutral Switzerland, but American officials worried that accepting her into the United States could damage its improving relations with Moscow. Finally, President Lyndon B. Johnson, on humanitarian grounds, agreed to admit her but asked that there be as little fanfare as possible.
<snip>
Her arrival in New York, in April 1967, was more triumphant than low-key. Reporters and photographers were waiting at the airport, and she held a news conference in which she denounced the Soviet regime. Her autobiography, “Twenty Letters to a Friend,” was published later that year, bringing her more than $2.5 million. In 1969 she recounted her journey from the Soviet Union in a second memoir, “Only One Year.”
Settling in Princeton, N.J., Ms. Alliluyeva made a public show of burning her Soviet passport, saying she would never return to the Soviet Union. She denounced her father as “a moral and spiritual monster,” called the Soviet system “profoundly corrupt” and likened the K.G.B. to the Gestapo.
Writing in Esquire magazine, Garry Wills and Ovid Demaris — under the headline “How the Daughter of Stalin Denounced Communism and Embraced God, America and Apple Pie” — said the Svetlana Alliluyeva saga added up to “the Reader’s Digest ultimate story.”
As the Kremlin feared, Ms. Alliluyeva became a weapon in the cold war. In 1968, she denounced the trial of four Soviet dissidents as “a mockery of justice.” On Voice of America radio, Soviet citizens heard her declare that life in the United States was “free, gay and full of bright colors.”
[/quote]
How about the first U.S. citizen to be canonized as a saint?
Mother Frances Xavier Cabrini.
How about the Irish-born labor activist Mary “Mother” Jones?
And while we’re discussing famous Soviet leaders whose kids became U. S. citizens, there’s also this:
Nina L. Khrushcheva, great-grand-daughter of Nikita: Immigrant of the Day: Nina Khrushcheva (Former Soviet Union) (publ. Oct. 19, 2007):
I’ll leave it up to the Interested Reader to research what may have happened to the intervening Khrushchev generations.
ETA: And now, the $64,000 question! How many sons/daughters/descendants/cousins/whatever of U. S. Presidents have become naturalized Soviet or Russian citizens?
Hedy Lamarr was famous before her naturalization. She became a US citizen in 1953. Most of her Hollywood films were made in the 1930s or 40s.
Martina was already an accomplished tennis player when she defected.
Hedy Lamarr was an inventor and patented a spectrum-hopping device that serves as a basis for modern spread-spectrum communication technology, such as Bluetooth, COFDM used in Wi-Fi network connections, and CDMA:
There are a number of prize-winning women writers who were born in other countries but I’m not sure of their current status, whether they’re naturalized, or green card holders. Some of them are married to US citizens:
Jamaica Kincaid
Edwige Danticat
Bharati Mukherjee
Jhumpa Lahiri
Bapsi Sidhwa
Monique Truong
I don’t know how many of these you’d count as “well-known”, though–Jhumpa Lahiri won a Pulitzer prize but she’s not really a household name.
I just remembered well-known author Isabel Allende, who became a US citizen in 2003:
Most people are more familiar with entertainers than with scientists or engineers; “engineer” isn’t something you get into “because I want to be famous!”.
Ayn Rand was a writer.
As it happens, I can find no confirmation online, incl. in her Wiki bio, that Catherine Zeta-Jones (born in Wales, UK) was ever naturalized. Thought she had been.
From this list, Category:Naturalized citizens of the United States - Wikipedia, I find these famous female naturalized U.S. citizens (some duplicates with names already mentioned - sorry):
Elizabeth Arden
Jacinda Barrett
Mischa Barton
Sarah Chalke
Charo
Anna Chenault
Claudette Colbert
Nadia Comăneci
Sheena Easton
Frances Fisher
Joan Fontaine
Greta Garbo
Greer Garson
Jennifer Granholm
Salma Hayek
Teresa Heinz
Iman
Margot Kidder
Heidi Klum
Madeleine M. Kunin
Nancy Kwan
Elsa Lanchester
Merle Oberon
Catherine O’Hara
Maureen O’Hara
Ileana Ros-Lehtinen
Isabella Rossellini
Ann Rutherford
Monica Seles
Orly Taitz
Jessica Tandy
Elizabeth Taylor
Ivana Trump
Rachel Weisz
Ruth Westheimer
Anna Wintour
Fay Wray
Nicole Kidman
Olivia Newton-John
Natalie Portman
?Diane Kruger?
?Brigitte Gabriel?
Audrey Hepburn
Isla Fisher
ETA both have been working and living in the US for years, but I don’t know if they are naturalized.