How does one unpack a tar file in Android?

I don't know if there is support for it built into the OS. But you should be able to use a third party library to do it.

Here is one, I am sure there are others to choose from out there as well.

Sorry for reviving an old question.

As of 6.0/Marshmallow, Android includes Toybox, an executable that contains small versions of every utility.

So on 6+ versions of Android, you can execute tar command as you would on a normal linux system.

As of Q1 2019, 6.0 and higher represent approximately 90% of Android users, so this is more or less safe to do unless you want full support, or are targeting a market with different Android adoption rates.