Digital labour platforms are transforming labour markets worldwide, and migrant workers are pivotal in this transformation. Drawing on a qualitative study in Chile, we uncover how Latin American and Caribbean migrants navigate and resist platform labour conditions, considering the algorithmically controlled and surveilled aspects of food delivery platforms, as well as the impact of migration status on their work. We contend that understanding migrant labour agency requires examining both the platforms' socio-technical structures and the host country's migration policies. These policies determine workers' migration status, shape their work experiences, and consequently impact their resistance to precarious labour conditions. We introduce the concept of migrant platform labour agency to illustrate the various forms of resistance migrants employ in navigating the platform labour market. This concept contributes to understanding the nuances in migrants' labour agencies, which range from acceptance to resistance, considering the interplay between the migration policy environment and platforms' socio-technical assemblage.