Under California law (Cal. Civ. §46),
Slander is a false and unprivileged publication, orally uttered, and
also communications by radio or any mechanical or other means
which...4. Imputes to him impotence or a want of chastity
You could hire an attorney to file a defamation lawsuit against the party. As part of the process, your attorney would file a motion to compel Twitter to supply information (such as IP address) which might maybe lead to the actual person. This article discusses the likely steps, but since Twitter is also in California, the first step is easier. Using an IP lookup tool, you could get the company that provided the connection, and then maybe the person, if it was not a Starbucks. Another court order may be required to compel e.g. Comcast to supply the individual's information.
Calling you a slut falls under the rubric of defamation per se, where it is assumed, by law, that you were damaged, so you don't have to prove that you were actually damaged.