This is everything you need to know about how to recruit Doc in Chrono Cross: The Radical Dreamers Edition.
How to Recruit Doc
The first decision that influences your ability to recruit Doc is when you have to choose whether to save Kid or not. If you choose to save Kid, Doc is not available to recruit. If you choose to leave her, you can then recruit Doc.
After the events of the S.S. Invincible, return to Guldove and visit the house where Kid is resting. Doc will offer to join to make amends.