Mr Mara, whose father Wellington once owned the team, said that winning the Oscar would be more of an achievement for his daughter than victory at the Super Bowl.
He confessed that he wept as he watched the announcements of the nominations on television.
"I wasn't expecting it," he said. "I knew she was somewhere on the bubble and I really don't know how these things work, so I let out a pretty loud roar. I cried for a while, then went to church and lit a few candles."
The Mara family has been linked to the Giants for some years. The team is an unlikely Super Bowl contender after struggling all season, and Miss Mara is similarly an outsider for the coveted trophy.
She will go up against with Meryl Streep, Glenn Close, Viola Davis and Michelle Williams at the award ceremony on February 25.
Mr Mara said he was happy that the event did not clash with the Super Bowl, which takes place on February 5. Earlier this month, he missed the Giants' play-off game against the Green Bay Packers in order to attend the Golden Globes with his daughter.
He said: "I know my daughter would want me to go to the Super Bowl, but I'm glad I don't have to make that decision."
Miss Mara has been praised for her dedication to the role of Lisbeth Salander in the acclaimed adaptation in the Swedish thriller.
Her father said that it was difficult to watch her in scenes depicting torture and rape, but that he was enormously proud of her acting ability.
He added: "It wasn't for the faint of heart, but Rooney blew me away by how good she was. I forgot it was my daughter, and that just proved to me she was Oscar-worthy.
"Rooney had to learn how to kickbox and ride a motorcycle and do so many physical things to get ready for the film. She showed a lot of toughness going through the whole experience."