I have an application, say gedit, which is dynamically linked and I don't have the source code. So I can not compile it as I like. what I want to do is to make it statically linked and move it to the system which doesn't have the necessary libraries to run that application. So is it possible to do it and how?
It is theoretically possible. You basically have to do the same job that the dynamic linker does, with some modifications, i.e.
So objdump, readelf, and objcopy will be some of your friends.
The task is not easy and the result will be neither automatic, nor (probably) stable.
You may want to check out this code by someone else that tried the same, by actually intercepting the dynamic linker (i.e. all steps above, except the last) and dumping the results to disk.
It is based on this tool, so it's anyone's bet whether it works on the newest kernels.
(It probably doesn't - and you need at least to patch it to reflect the new structures. This is my attempt at doing so. Caveat emptor).