At the moment, you can use a little hack. If you annotate your Specs2 class as follows:
@RunWith(classOf[JUnitRunner])
With older versions of specs2, this should be:
@RunWith(classOf[JUnitSuiteRunner])
The Scala IDE can run it with the JUnit runner simply through the popup menu (see the details here).
I'm working on a Specs2 plug-in for the Scala IDE (well, unfortunately I haven't really found time for it for a while, but it's still on my list).
It has a working version for the previous version of the Scala IDE, it is a bit difficult to set it up but works. See the details here: http://rlegendi.github.io/specs2-runner/