Carmen Romano de Lopez Portillo, wife of the new president of Mexico, was the only member of a reigning family in world politics to be invited to the Carter Inauguration, and she wasn't hard to spot.

Huge eyes with great blue eyelids drawn above them at a slant; long, bouncing black curls; giant diamond-and-enamel necklace and matching mobile ring; bright red, tight-fitting suit with fur collar, and matching pumps. "The living representation of her homeland," the secretary general of the Organization of American States, Alejandro Orfila, called her yesterday at a luncheon in the Pan American Union.

Ordinarily, heads of state and their families are not invited to presidential Inaugurations, but are represented by their ambassadors, which makes life and protocol much simpler.

But Mrs. Lopez Portillo was invited by Rosalynn Carter (who had attended her husband's inauguration in Mexico City on Dec. 1) and made the rounds here with her children, Paulina, 17; Carmen, 21; Jose, 22, and Jose's fiancee, Mariso Velazco.

They had breakfast yesterday with Mrs. Carter at the White House, before meeting diplomats at the Pan American Union luncheon, where Orfila gave a long poetic toast to her about "A new man . . . through his wounds, his suffering and his sacrifices, he became a people. And he was called Mexico."

A friend and consultant of Mrs. Lopez Portillos's who happened to be in town, Israeli psychic Uri Geller, was not able to make the luncheon as he is doing the rounds here as the date of Jack Carter's sister-in-law. But seer Jeane Dixon, who has known the Mexican First Lady for some years, did make it.

Mrs. Lopez Portillo holds cabinet status as president of the Mexican foundation for the development of children and the family.