BEIJING — He has a lakeside villa valued at more than $3 million, two Mercedes sedans in the garage and a butler who fluffs his pillows and shines his shoes.

But Liu Xiyu, a real estate executive in Beijing, still lacks the convenience he says he most wants in life: an American green card.

Fed up with China’s rampant air pollution and the rigid school system his children endure, Mr. Liu pledged $500,000 to a California housing development last year in hopes of obtaining a special visa for investors, known as EB-5, which would allow his family to spend more time in the United States.

Now, President Trump’s vow to tighten immigration policies and new scrutiny after a series of fraud and abuse scandals have spurred thousands of Chinese applicants like Mr. Liu to seek a visa before more stringent requirements can be put in place.