Accounting is both art and science—but in a bid to help more foreign accountants work in the U.S., it is the science part that the accounting industry wants to emphasize.

Major accounting firms and the industry’s trade group are trying to convince Congress to include accounting as part of the “STEM” career fields—science, technology, engineering and mathematics. Those areas get special consideration when the U.S. government determines which foreigners get visas to work in the U.S.

Specifically,...