I live in a apartment complex in CALIFORNIA. When I moved in my carpet was only cleaned, it is a terrible old carpet.
I heard once that as a TENANT I have the right to get my carpet cleaned once a year for Free (it should be paid by the landlord). I want to know if this is my right.

That is "urban legend". I've yet to find a state that names this as a "right" - or landlord requirement.

Ask nice, though. You might be surprised. I frequently offer carpet cleaning to longer term residents as an incentive to renew their lease. It's a win-win for both me and the residents.

100% Myth the ONLY time you can by law get the carpeting replaced is =IF= the carpet is naturally worn threw where it causes a trip and fall sitch. It's in the health codes for the state of California and I believe all states in the USA. =IF= you make the mistake of damaging the carpet to make it a trip and fall / health code violation you will most likely be CHARGED for the carpet replacement. Yes you can always ask. There are several other types of flooring
that wear far better than carpeting. If your landlord doesn't want to get involved with changing or cleaning the carpeting then you have a choice. You can give your 30 day notice if you have a month to month agreement and move
some where else. You can have the carpet cleaned or clean it yourself. Or some times a area rug works wonders to the over all look and feel of your living space. Plus! You can take it with you when you move on! Win Win.

I live in a apartment complex in CALIFORNIA. When I moved in my carpet was only cleaned, it is a terrible old carpet.
I heard once that as a TENANT I have the right to get my carpet cleaned once a year for Free (it should be paid by the landlord). I want to know if this is my right.
Sorry - cleaning the carpet is the tenant's responsibility. No professional carpet cleaner will move your furniture and be responsible if something is broken... think about it.