I'd fire him. If Twitter doesn't fire him they are spoiling their pool of potential hires. Who would want to work with this guy? I bet the female employees at Twitter are already fairly creeped out by him now.
As others have stated, employment in California really is at-will. For example, I know someone who has been fired for getting too drunk at a company party!
So yeah, companies in California can fire you for any reason, or no reason at all. In this case I see the negative effects of keeping the person employed (such as the loss of potential employees and damage to the company reputation) outweighing their value as an employee.