If you’re 60 or older and a citizen, temporary, or permanent resident, you can use your CURP number to register for the Covid-19 vaccine. Debate Media has posted a handy guide in Spanish (https://www.debate.com.mx/politica/Como-registrar-a-un-adulto-mayor-para-recibir-vacuna-contra-Covid-19-Secretaria-de-Salud-explica–20210202-0040.html). Following is a google translated copy.
Note that I haven’t been able to get the website to load. Perhaps they’re doing maintenance, or it’s just overwhelmed. Your mileage may vary, and it’s not a bad idea to just keep trying every now and again.
Disclaimer: This information is provided as a guide only and I don’t warrant it to be complete or accurate in any manner. As with anything concerning your health, please do your own research. Please refer to the originating website (https://www.debate.com.mx/politica/Como-registrar-a-un-adulto-mayor-para-recibir-vacuna-contra-Covid-19-Secretaria-de-Salud-explica–20210202-0040.html) for clarifications or further information.