Rose Lutian was 103 years old yesterday, and for her birthday she got the present that she has wanted for the last year - her United States citizenship.

It has been 75 years since she left a small farming village in Hungary to go to the mining country of West Virginia and watched four generations of her family grow up around her. Yesterday, as they sang a hearty happy birthday in her honor in the small white frame house in Alexandria, she said she could die at peace now, because the earth would no longer be receiving a stranger.

Although she cannot read or write, and speaks broken English, there was, it turned out, a narrow niche in the law just wide enough to receive her. Because she had been in this country at least 20 years when the current naturalization law was passed in 1952, and because she was older than 50 by then, she was exempt from the literacy requirements that govern those seeking citizenship.

She had come to his country in 1903 because her husband was here, she said simply, and she knew that he would provide for her. But there was an accident in the No. 10 mine near Wilco, W. Va., in 1917, and he was paralyzed from the waist down, and so she was the one who did the providing.

The mines claimed two of her sons as well, and of the 10 children she bore, only three are still living. Now, however, there are 16 grandchildren and 32 great-grandchildren and two great-greatgrandchildren. The small, pink flowers on breast trembled as many of them crowded around yesterday and toasted her as the sun streamed through the living-room windows.

Most of the family lives in the Del Ray section of Alexandria now, as they have for the past 30 years, after another migration in Mrs. Lutian's family. "I knew I was not going to raise my children in the coal mines," said Rose Lutian's daughter, Mary Yuhasz. "I took drastic steps. I came here and just hoped my husband would follow.

He did follow, and went to work for the city of Alexandria. Now their daughter, Barbara-Hearn, has moved her family to Fredericksburg. Yet another escape - this one from the schools and increasingly urban atmosphere of suburban Washington.

Now 13-year-old Chris Hearn looks about the living room, and listens to the medley of murmurs, sighs and laughter that are the songs a large family sings, and says he's not so sure he likes being a part of such a big group. "Too many people," he says with teen-aged brashness, but an uncle shakes his head and smiles. "You'd have liked it in the coal country," he said. "All the miners had big families. You need each other then."

Rose Lutian sits quietly, her eyes wide in a small, creased face and watches while her daughter tells her story. Mary Yuhasz tells how her mother worked hard to raise them all, how she couldn't get by on the $52-a-month pension the company provided, and how she kept a small store and took in boarders, raised vegetables and helped the miners' wives give birth to their babies, to keep her family together.

Yesterday she wore a pale blue dress and watched the antics of her 2-year-old great-grandchild. Her parish priest had brought her holy communion and she said "God bless you" to all who came to wish her well. But for the most part she sat and watched.

"She says sometimes, 'I wish I could tell you what I've learned, I wish you would listen," her daughter said. "And I say, 'but Nana, this is my time now, your time is past, we have to change with the times."

There is a big, wooden crucifix above Rose Lutian's bed and delicately colored photographs of her two sons in their mining hats on her wall. "She had a hardship, you know," her daughter said. "But she survived."