My situation

My machine

$ lsb_release -a
No LSB modules are available.
Distributor ID: Ubuntu
Description:    Ubuntu 14.04 LTS
Release:    14.04
Codename:   trusty

The latest rsync version to compile (for me it was rsync-3.1.0.tar.gz)

$ curl -s http://rsync.samba.org/ftp/rsync/ \
    | sed -r 's/^.*href="([^"]*)".*$/\1/' | grep 'rsync-[0-9].*\.tar\.gz$'

Procedure

1. save the tarball name in a variable

   $ RSYNCTGZ="rsync-3.1.0.tar.gz"
   

2. install needed software

   $ sudo aptitude install gcc-arm-linux-gnueabi
   

3. download sources

   $ wget http://rsync.samba.org/ftp/rsync/$RSYNCTGZ
   $ tar xzf $RSYNCTGZ
   $ cd rsync-[0-9]*
   

4. compile

   $ ./configure --host=arm-linux-gnueabi CFLAGS=-static
   $ make
   

5. install on the device

   $ adb push rsync /data/local/tmp && adb shell chmod 775 /data/local/tmp/rsync
   

6. test execution

   $ adb shell /data/local/tmp/rsync
   

References

• stackoverflow