When News Corp. officials gathered in the Hong Kong convention center in March to unveil their latest Chinese Internet investment, a tall woman in their midst handed out a business card that read simply, “News Corporation/Wendi Deng Murdoch.” Ms. Deng is not a News Corp. employee. Once a junior executive at the company’s Star TV unit in Hong Kong, the 31-year-old Ms. Deng quit her post before marrying News Corp. Chairman Rupert Murdoch last year. Since then, she has been portrayed—by Mr. Murdoch and the company—as a traditional housewife who attends to decorating, her husband’s diet and the like. But Ms. Deng is no homebody.