Nope since since January 1, 2024:Yep. But Aqua lab aquaria sells it is that legal????

Legislative Action: Banning Caulerpa to Protect Our Coast - Orange County Coastkeeper
Starting today, January 1, 2024, Californians are prohibited from selling, possessing, importing, transporting, transferring, releasing alive in the state, or giving away without consideration all saltwater algae of the genus...

Starting today, January 1, 2024, Californians are prohibited from selling, possessing, importing, transporting, transferring, releasing alive in the state, or giving away without consideration all saltwater algae of the genus Caulerpa, except that in possession for bona fide scientific research.
The new statewide ban on Caulerpa is due to Assembly Bill 655, which was signed into law by Governor Newsom on July 27, 2023. The bill was introduced by Assemblywoman Cottie Petrie-Norris (D-Irvine) with the help of our team and the California Coastkeeper Alliance.
The Californian coast has suffered from several costly and damaging Caulerpa algae invasions, including one currently disrupting Newport Bay. The most likely cause of these infestations is illegal dumping of aquarium water containing Caulerpa. With the statewide ban in effect, we can prevent further outbreaks along our coast.