Solicitation of a prostitute falls under Cal Pen Code § 647, Disorderly Conduct as every person:
Who solicits or who agrees to engage in or who engages in any act of prostitution. A person agrees to engage in an act of prostitution when, with specific intent to so engage, he or she manifests an acceptance of an offer or solicitation to so engage, regardless of whether the offer or solicitation was made by a person who also possessed the specific intent to engage in prostitution. No agreement to engage in an act of prostitution shall constitute a violation of this subdivision unless some act, in addition to the agreement, is done within this state in furtherance of the commission of an act of prostitution by the person agreeing to engage in that act. As used in this subdivision, "prostitution" includes any lewd act between persons for money or other consideration.
This is a misdemeanor and is therefore is prosecuted pursuant to Cal Pen Code § 802 (Time period for commencement of prosecution):
(a) Except as provided in subdivision (b), (c), or (d), prosecution for an offense not punishable by death or imprisonment in the state prison shall be commenced within one year after commission of the offense.
SEC. 225. SOLICITING PROSTITUTION PROHIBITED.
It shall be unlawful for any person on any public street or highway or elsewhere, to solicit, by word, act, gesture, knock, sign or otherwise, any person for the purpose of prostitution.
(Added by Ord. 1.075, App. 10/11/38)
SEC. 226. PENALTY.
Any person violating the provisions of Section 225 of this Article shall be guilty of a misdemeanor, and upon conviction thereof, shall be punished by a fine not to exceed $100, or by imprisonment for not more than 50 days, or by both such fine and imprisonment.
I hope that helps. Please let me know if you need anything else.