playframework uses sbt to manage dependencies. just add twitter4j dependency in your build.sbt file and it will be downloaded and added to classpath.
add dependency in your build.sbt like below
libraryDependencies += "org.twitter4j" % "twitter4j-core" % "2.1.4"
Please see below link
http://www.playframework.com/documentation/2.2.0/SBTDependencies