The good news for employers is that plenty of qualified employees around the world are eager to come to the U.S. A recent survey of 27,000 digital workers by Boston Consulting Group of found that two-thirds said they would be willing to leave their home country for the right job. That percentage is much greater than in other fields.

Workers who said they were open to moving were most likely to cite the U.S., followed by Canada and Germany, as desired destinations.

Of course, hiring an immigrant is not just a matter of what the employer and employee want. The U.S. government can make things very difficult. In recent years, it has increasingly exercised that right.

In the fourth quarter of 2016, at the end of the Obama administration, 92 percent of applications for H-1B visas were approved. That dropped to 83 percent in the final quarter of 2017 and 75 percent at the end of 2018.

H-1B visas are granted to employers to bring skilled employees to the U.S. The visa is typically good for three years and can be extended another three years. The visa is tied to the employer; if the worker's employment ends, he or she must leave the country.

At the same time, demand for workers in AI has skyrocketed. AI-related job postings increased 159 percent in the past 12 months, according to an analysis of Labor Department data by CompTIA, an IT trade association. The organization estimates there are 700,000 unfilled AI-related jobs in the U.S.

Read more: 

• Higher-skilled workers more likely to leave when firms automate
• Americans expecting AI to change their workplace
• Employers will need to hire for digital skills talent to survive