To do that, you need to grab the corresponding .deb package that was compiled for your OS version. If you're using Ubuntu like me, go to one of its Archive Mirror. In this case, we are going to http://us.archive.ubuntu.com/ubuntu/.

Ubuntu mirror archive
Access /pool/main/a/apt/ path and you'll see a bunch of .deb package. Select the one that is suitable with your architecture (and64/i386)

select apt deb file
Once it finishes downloading, you can install apt DEB file by running the following command :

sudo dpkg -i /path/to/apt_deb_file.deb
Remember to replace the /path/to/apt_deb_file.deb with the path of the file you've just downloaded.