In CA if there is no contract singed by both parties only estimated price, can contractors

The lack of a written contract in of itself does not necessarily preclude a contractor from the right to record a lien if it otherwise would be able to. The contractor will need to be able to demonstrate that the work performed was authorized and that they are properly licensed, among other things. But liens pursuant to verbal agreements have been enforced by courts in this state. 

Yes, if you improved the property a lien may be recorded for the reasonable value of the work - written contract or not.