Visa policies to retain United States-trained STEM PhDs are of central importance to national innovation and economic competitiveness. There is also growing interest in "startup" visas that stimulate entrepreneurial activity and job creation, particularly in technology sectors. However, there is little understanding of how visa policies might influence foreign PhDs' employment in technology startups. This study investigates differences between 2,324 foreign and US PhDs from US research universities using a longitudinal survey of individuals' preferences and characteristics during graduate school and their subsequent employment in a startup or established firm. Among PhDs whose first job is industrial research & development, 15.8% of US PhDs work in a startup compared with 6.8% of foreign PhDs. Foreign PhDs are as likely as US PhDs to apply to and receive offers for startup jobs, but conditional on receiving an offer, they are 56% less likely to work in a startup. This disparity is partially explained by differences in visa sponsorship between startups and established firms and not by foreign PhDs' preferences for established firm jobs, risk tolerance, or preference for higher pay. Foreign PhDs who first work in an established firm and subsequently receive a green card are more likely to move to a startup than another established firm, suggesting that permanent residency facilitates startup employment. These findings suggest that US visa policies may deter foreign PhDs from working in startups, thereby restricting startups' access to a large segment of the STEM PhD workforce and impairing startups' ability to contribute to innovation and economic growth.