Background: A sustained period of social, economic, and political unrest took place during October of 2019 in Chile. As an institutional solution, the “Agreement for Social Peace and the New Constitution” was signed. In this document, most political parties committed to reestablishing peace and public order in Chile, agreeing on the initiation of a constitutional process. To promote participation of civil society actors, the “Popular Initiative for Norms” was enabled. This was a platform where civilians could submit proposals for constitutional norms to be discussed by the Constitutional Convention. We aimed to analyze proposals related to migrants and migrant health. Methods: We conducted a qualitative thematic analysis of the proposals. Sixteen of them were related to migrants, and we analyzed their association to health. We also evaluated their link to the Health Goals 2030 set out by the Chilean Ministry of Health and the Global Action Plan 2019–2023 for Promoting the Health of Refugees and Migrants by the World Health Organization. Results: Four main thematic categories were identified: 1) Humans rights of migrants, refugees, and asylum seekers; 2) Nationality and regularization of migrants and refugees; 3) Political participation and cultural integration of migrants and refugees; and 4) Specific regulations on slavery and human trafficking. These resonated with broader frameworks established in the Health Goals 2030 (Chile) and the Global Action Plan 2019–2023 for Promoting the Health of Refugees and Migrants by the World Health Organization. Conclusions: The ‘Popular Initiative for Norms’ was a non-binding participatory mechanism. Although the proposals sent through were not guaranteed to be included in the constitutional draft—and despite the final draft being rejected last September 2022—the platform allowed to gain insights into civilian opinions. Our findings showed that there is an incipient yet weak recognition of the rights and situation of migrants in Chile. There was no direct mention of health nor an explicit contemplation of social determinants of health. Despite there being an urgent need to define strategies for migrants’ health in Chile, this study demonstrated that civil awareness and interest are still insufficient.