Don't refactor it right away. I'll take your word that the code is shit (frequently the case), but you don't know the idiosyncrasies well enough to know what to do with it.
After you've worked with the code a while, you'll be able to attempt a large refactor. Until then, gather low hanging fruit. Clean up confusing variable names. Add comments where needed. Write your new code as clearly and cleanly as possible. Use a tool like sonar to inspect your new code so that you don't introduce new problems.
Most importantly, ADD UNIT TESTS. That will make sure that your new code works with the old and it will allow you to attempt a larger refactor while being sure that you aren't breaking anything.
If necessary, you may need to add some integration tests as well.
I've been in your shoes. Bad code is no fun, but don't let it get you down. Focus on the happy parts of your job (team, culture, whatever). Good luck!