There are several issues.
Firstly, some simple ones: it should be publication in a journal, not on; and the process as a whole is usually called peer review, not peer reviewing. [Edit: a third "correction" removed after Colin Fine convinced me it's not needed.]
Secondly, the form …requires to go through… is incorrect. Requires is never followed by just an infinitive in English — it can be followed by either a gerund (the necessary action), or a noun phrase plus an infinitive (the person/thing who has to do the action, plus the action):
Joining the army requires passing a physical exam.
Joining the army requires you to pass a physical exam.
Thirdly, as Adam points out, there’s a slight clash in your sentence between the verbs bringing (whose subject is the author) and go through (whose subject is the paper itself). Given the form of the sentence — the verbs aren’t literally parallel — this isn’t quite a matter of grammar (to my ear) so much as of meaning. Something like
Bringing an article from draft to polished publication in a scientific journal requires it to go through a process called “peer review”.
is grammatically quite correct, parallel to eg:
Sending your daughter into the army requires her to pass a physical exam.
But it’s a slightly awkward phrasing, making a shift in agent that really isn’t necessary. So in the end I’d suggest something like:
Bringing an article from draft to polished publication in a scientific journal requires putting it through a process called “peer review”.