HelloLibtorrent
This is a basic setup to test libtorrent on android.
You can simply run the clean-and-build.sh to build the entire thing. This will also automatically install the created apk on a connected phone and start adb logcat.
Do note that this example will download a torrent file which is hardcoded on a location (see jni/hello.cpp for details). You will have to place this torrent file manually on your phone. Next, you will want to change the 2 occurrences of /storage/sdcard0/Torrents in jni/hello.cpp to where the torrent is located.