how to get accepted back into a phd program in the US?
The best way to find out if you stand a strong chance of being reaccepted is to get into direct communication with the director of graduate studies or admissions.  (E-mail communication is okay, but talking on the phone would be better.)  That is the person who is best informed about what your chances are.

You may have just gotten a boilerplate answer from a departmental administrator that, since you are no longer a student, you automatically need to re-apply.  While that is undoubtedly true, strictly speaking, it may not be particularly useful information.  The faculty member(s) dealing directly with graduate admissions may be able to tell you a lot more.  Depending on the department, readmission might be a mere formality; or you might be competing on even footing with all the new students who are applying at the same time; or it could be somewhere in between.

If you are intending to continue working under the same advisor you had for your masters thesis, you should contact the advisor as well.  In many departments, if your advisor really wants you, admission can be pretty much guaranteed.  This is especially true if the advisor knows you, has worked with you, and wants you back.