My parents moved to US and applied for green card. They plan to get advanced premium tax credits to buy insurance on marketplace. Can we use ITIN to file taxes?

You have to have a SSN to apply for marketplace insurance coverage. 

@ashutoshchetal here are the minimum requirements for Marketplace. 

https://www.healthcare.gov/quick-guide/eligibility/

applying for a Green Card is below the minimum requirement..review this link for immigrant eligibility

https://www.healthcare.gov/immigrants/immigration-status/