It is unfortunately legal. The information about your arrest no doubt originally appeared as a public record on an official government site or it could have come from a newspaper mention of the arrest. There are ways to deal with this, but I can not give you any specifics. I'm going to edit your question to the Practice Area "Internet" which is where this question has been addressed quite a few times in the past. I hope the change will get you the sort of information and guidance you want.
Public record, unfortunately, but you can always attempt to seal your arrest record under Penal Code section 851.8. Consult with a locally experienced criminal defense attorney who can assist.
Law Offices of David Shapiro 3555 4th Avenue San Diego, CA 92103 (619) 295-3555
You can demand a written certificate from the arresting law enforcement agency pursuant to California Penal Code Sections 851.6. and 849.5 that the "arrest" is a detention only because no charges were brought. In fact, an arrest becomes a detention only by operation of law when no charges are brought although that may happen upon the running of the statute of limitations. With a certificate from the arresting agency that your arrest was a detention only, the website may be willing to remove the entry.
If necessary, you may want to use the Avvo search features to pull up the many previous Q and A posts pertaining to mugshots.com. The issues are very similar. A few attorneys who have posted on that issue claim to have had some success at compelling removal, and you may want to reach out to some of them.
My responses to questions on Avvo are never intended as legal advice and must not be relied upon as legal advice. I give legal advice only in the course of an attorney-client relationship. Exchange of information through Avvo's Questions forum does not establish an attorney-client relationship with me. That relationship is established only by individual consultation and execution of a written agreement for legal services.
As Attorney McCall notes, many people have asked a very similar question and received some optimistic responses. You can read those questions and answers via the link below.
The above is general information ONLY and is not legal advice, does not form an attorney-client relationship, and should NOT be relied upon to take or refrain from taking any action. I am not your attorney. You should seek the advice of competent counsel before taking any action related to your inquiry.