In short, No. Some local rent control ordinances, however, do require the installation of new carpet after a certain time frame. For example, West Hollywood requires the landlord to install new carpet every 7 years.
However, under California law if the carpet is torn, the landlord is required to repair/fix/replace that portion of the carpet that has worn through.
Disclaimer. The information posted above is for general information, does not constitute professional legal advice, and does not create an attorney client relationship.