Yes, but no. The civil action you are thinking of is called Libel. This happens when a person tells damaging lies about you. The problem is that you would have the burden of proof (by a preponderance of the evidence in a civil case, meaning more likely than not) that she was lying. In terms of an attempted rape, this is probably impossible.
The type of attorney who would take such a case is generally reffered to in th biz as a PI or Personal Injury attorney. Check AVVO for your area (I know, shameless plug for the site).
I should also note that the fact that your son and this girl were not having intercourse does not necessarily mean that he is not guilty of a sex crime. It mostly depends on the girl's age.
If you can get the DA to "go for" the crime of filing a false police report, and if the state prevails, restitution may be possible.
Curt Harrington Patent & Tax Law Attorney Certified Tax Specialist by the California Board of Legal Specialization PATENTAX.COM This communication is general information and not legal advice, and does not create an attorney-client relationship. This communication should not be relied upon as any type of legal advice. Please note that no attorney-client relationship exists between the sender and the recipient of this message in the absence of either (1) a signed fee contract and (2) remission of an agreed-upon retainer. Absent such an agreement and retainer, I am not engaged by you as an attorney, nor is any other member of my law firm.
It appears that at present your son is a Defendant in a criminal case. Your focus should be on his defense and acquittal.
Once acquitted you have opened up avenues for malicious prosecution and emotional distress damages claims. Of course you will need DA to take a reverse course to charge her with filing a False police report. A lot will depend on how you can get her to admit to perjuring herself.