This is a basic setup to test libtorrent on android.
Before building, make sure to create a project out of the cloned folder:
cd HelloLibtorrent
android update project -p . -t android-14
You can then run the clean-and-build.sh script to build the entire thing. This will also automatically compile and create the .apk file.
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 and where the resulting files should be stored.