I'm a US citizen and want to sponsor my parents for green cards, but they’re currently in the US on visitor visas.

Ensure they do not overstay their authorized stay period while applying

File Form I-130 and Form I-485 concurrently if they entered lawfully.

Yes, you can sponsor them by filing Form I-130 and they may apply for a green card through adjustment of status while in the U.S., if eligible.