Yeah, Linux is just the kernel, and android a layer on top of it with a GUI, anyway you can easily have a terminal open on a cellphone or even from a PC do a "adb shell" command and you're in it, top, mkdir, cd, etc. If you are root, install busybox and all.
I guess OP wants to install a full distro on his cellphone?
It's possible to install a complete GNU/Linux software stack on Android devices, e.g. by adding a chroot environment as others already have implemented. This kit does 2 things differently: Firstly, it installs a Debian file system side-by-side to the Android file system. In order to access anything that's accessible from Android also from the Debian side. And secondly, the Debian bootstrap is executed on the Device itself without any help of a larger PC, Android debugging bridge or similar.
UserLAnd
Easiest way to run GNU/Linux Distros on Android - no root required
UserLAnd is an open-source app which allows you to run several Linux distributions like Ubuntu, Debian, and Kali.
No need to root your device.
Use a built-in terminal to access your favorite shells.
Easily connect to VNC sessions for a graphical experience.
Easy setup for several common Linux distributions, like Ubuntu and Debian.
Easy setup for several common Linux applications, like Octave and Firefox.
A way to experiment and learn Linux and other common software tools from the palm of your hand.
UserLAnd was created and is being actively maintained by the folks behind the popular Android application, GNURoot Debian. It is meant as a replacement for the original GNURoot Debian app.
When UserLAnd first launches, it presents a list of common distributions and Linux applications. Clicking one of these then leads to a series of set-up prompts. Once these have been completed, UserLAnd will download and set up files required to start the task that has been selected. Based on the set-up, you will then be connected to your Linux distribution or application in a terminal or VNC viewing Android application.