WASHINGTON (AP) _ The wife of billionaire Jack Kent Cooke was arrested Monday by the Immigration and Naturalization Service after she lost an appeal of her deportation order.

Marlena Ramallo Chalmers Cooke, who pleaded guilty in 1986 to a drug trafficking charge and served time in a federal penitentiary, was taken into custody without incident at her apartment in Alexandria, Va., said INS spokesman Duke Austin.

Last week, she lost her appeal of the deportation order originally issued in 1988, before she married the owner of the Washington Redskins football team.

U.S. District Judge Claude M. Hilton ordered her released on $50,000 bond pending another hearing, said INS spokesman Verne Jervis.

Jervis said the agency considers Mrs. Cooke deportable because she left the country voluntarily while she was under the deportation order, negating her right to remain in the country. He said she would have an opportunity to appeal a decision after the hearing.

''She's been here lawfully and we're going to file the appropriate court proceedings, if they have to be filed. I'm not going to get into the merits of things. She was at all times lawfully here,'' said her attorney, Robert Bennett.

Mrs. Cooke, about half the age of her 81-year-old husband, has made headlines by mysteriously shooting herself in the hand, driving through Georgetown with a man she identified as her nephew clinging to the hood of her car, and throwing a high-heeled shoe at a police officer who stopped her that night.

Cooke last month contended that his May 5, 1990, marriage to the Bolivian- born woman was not valid. He contended that the quickie Dominican Republic divorce obtained in 1986 by her former husband - Houston oilman David Chalmers - was illegal.

Marrying a U.S. citizen does not prevent a deportation, Austin said. Any noncitizen who commits a serious crime in the first five years - or two crimes in more than five years - can be deported, he said.