This essay brings together scholarship in biometrics and disability studies with conversations in transnational rhetorical studies to build a theoretical framework that examines the (re)emergence and (re)circulation of biometric screening technologies and attends to the role of technologies in theorizing an ethics of encounter. I argue specifically that tracing biometrics—discursive, material, and technological practices—reveals how such discourses and their promises materialize on bodies of refugees and shape their encounters as “others and other-others.” Using this framework, I analyze rhetorically cultural artifacts that circulated following the 2015 and 2016 terrorist attacks in Europe and the United States to demonstrate how biometric screening discourses of progress have participated in immobilizing refugees physically and exacerbating conditions of biopolitical control and debilitation.