I mean, not officially. There's nothing in the API documentation, and all my attempts to contact Twitter on this matter have been ignored. If you're getting abuse on Twitter you have to use the official Twitter clients to report people. No matter that 3rd party clients may be better at protecting your privacy, offering you a sanitised view of the people tweeting you, or enable you to block offensive words or phrases.
In Twitter's increasing war on the developers who helped build it, they simply won't allow unofficial clients to implement this basic functionality.
The nearest you can get to providing this service to users is to throw them out to the official mobile website, directly to the report page.
This, of course, ignores the fact that Twitter's mobile site may not work on the user's phone and may be blocked or monitored.
The problem of online abuse isn't unique to Twitter. They realise that the majority of their visitors come to watch - and only rarely interact. The big draws for these passive observers isn't their friends; it's "celebs". If those celebs get driven off by abuse, will the userbase migrate elsewhere?
Twitter could have harnessed the power of its 3rd party developers, it could have set up crowd sourced monitoring, it could have behaved like a good Internet citizen and worked with their community.
Instead they've done the bare minimum to appease the baying masses without trying to understand or fix their underlying problems. They've lost the trust of their 3rd party developers, lost the trust of those being abused, and will soon - I imagine - lose the trust of their star attractions.
Oh well. Fun while it lasted.