In a letter to state lawmakers, Schwarzenegger demanded they take action to address the situation and change the law, the Los Angeles Times reported Saturday.
Under current regulations, people convicted of such crimes as rape, murder and elder abuse are eligible to be paid to provide services for some of the most vulnerable Californians in their residences under the state's In Home Supportive Services Program, the Times said.
At least 210 workers and applicants with felony convictions flagged by investigators as unsuitable for the program are scheduled to resume or begin employment, state data shows.
"I am hard pressed to imagine that any member of the Legislature would allow a convicted sex offender to take care of their own grandmother in a nursing home," Schwarzenegger wrote the Legislature.
Officials at SEIU California, which represents more than 300,000 homecare workers, embraced the governor's call for action.
"Putting vulnerable adults in harm's way -- either through cutting needed services or by exposing them to dangerous individuals -- is unacceptable," SEIU California President Bill A. Lloyd said, "and we are committed to working with the Legislature and the administration on any measure to increase their safety, health, and well-being."