Yes, an oral agreement is enforceable in California unless it violates the statute of frauds, which states that certain contracts must be in writing. The statute is below:
Cal. Civ. Code 1624 [Statute of Frauds]
The following contracts are invalid, unless they, or some note or memorandum thereof, are in writing and subscribed by the party to be charged or by the party's agent:
(a) An agreement that by its terms is not to be performed within a year from the making thereof.
(b) A special promise to answer for the debt, default, or miscarriage of another, except in the cases provided for in Section 2794.
(c) An agreement for the leasing for a longer period than one year, or for the sale of real property, or of an interest therein; such an agreement, if made by an agent of the party sought to be charged, is invalid, unless the authority of the agent is in writing, subscribed by the party sought to be charged.
(d) An agreement authorizing or employing an agent, broker, or any other person to purchase or sell real estate, or to lease real estate for a longer period than one year, or to procure, introduce, or find a purchaser or seller of real estate or a lessee or lessor of real estate where the lease is for a longer period than one year, for compensation or a commission.
(e) An agreement which by its terms is not to be performed during the lifetime of the promisor.
(f) An agreement by a purchaser of real property to pay an indebtedness secured by a mortgage or deed of trust upon the property purchased, unless assumption of the indebtedness by the purchaser is specifically provided for in the conveyance of the property.
(g) A contract, promise, undertaking, or commitment to loan money or to grant or extend credit, in an amount greater than one hundred thousand dollars ($100,000), not primarily for personal, family, or household purposes, made by a person engaged in the business of lending or arranging for the lending of money or extending credit. For purposes of this section, a contract, promise, undertaking or commitment to loan money secured soley by residential property consisting of one to four dwelling units shall be deemed to be for personal, family, or household purposes.
This section does not apply to leases subject to Division 10 (commencing with Section 10101) of the Commercial Code.