Do I have to have a social security card to apply for an ID card in Shenzhen?

Not necessarily, but it is ok to pay social security locally in Shenzhen.

Application conditions:

Meet one of the following application conditions, should be handled:

(1), legally and stably living in this city (continuous residence registration for 3 months).

(2) Employment (social insurance has accumulated for 3 months in the past year).

(3), in the city's primary schools, secondary schools, full-time universities to study legally (with student status files and proof of reading).