Yes, your sister can be placed out of state into your care, but there are possible barriers for the to happen immediately.
Your sister is old enough to emancipate herself from the system, but that may not be her best course, depending on the outstanding warrants and possible charges. If the charges are felonious, she may be in the state for quite some time. If they are misdemeanors, depending on the severity, the judge can dismiss into your care.
I would suggest that you find out if she has a warrant. Have your sister go and get a police clearance. They normally cost anywhere from $3 to $20.
I would also suggest you contact the Ombudsman and DHHS OIG to report questionable activities. If you have been cleared for placement in your state, there should be no reasons why the agency will not transfer your sister to your care.
In most cases such as this, an agency will knowingly continue to keep a child in the care of the state instead of placing with a relative because the child generates more revenue for the agency and the state. Some authorities will call these questionalble or improper payments, and some authorities will call these revenue-maximizing schemes fraud. I prefer the latter.
California is currently under federal investigation for these types of fraud schemes. Take this opportunity to expose the system for what it is. Report them.