I was actually looking into the same thing today and got it working with my scala project (which uses SBT, though I've been running stuff through intellij). I think you're going to have to do a few things:
As mentioned here, you'll want to add a -javaagent:~/path-to/aspectjweaver.jar for whatever java command you are running. See here for an example of how to add the javaagent flag for a play project.
Include some extra dependencies:
libraryDependencies += "org.aspectj" % "aspectjweaver" % "1.7.2"
libraryDependencies += "org.aspectj" % "aspectjrt" % "1.7.2"
libraryDependencies += "com.jcabi" % "jcabi-aspects" % "0.8"
libraryDependencies += "com.jcabi" % "jcabi-log" % "0.8"
Create a META-INF/aop.xml in your resources folder for your project. This is what defines the runtime weaving for aspectj. See this gist for an example.
Copy the MethodLogger class from jcabi-aspects v0.8 (and Mnemos.java and NamedThreads.java) into your com.yourcompany.yourpackage. The reason for this (as far as I can tell) is that the jcabi packages are compiled in a special way, and we want to do run-time weaving instead, so this gets around that. Edit: perhaps this is due to me using Java 7 and the plugins being compiled in Java 6--I see some warnings when building in SBT.
I'd be happy to hear if someone has a better way, but this at least seems to work.