Online master's degree in CS at the Georgia Institute of Technology I am a working student (working in software engineering) and this year I'll be completing my CS Bachelor's degree in Italy. I am doing the online degree as I can't attend lectures, due to my job. 

I would like to continue my studies with a Master's Degree in CS so I googled a bit and found out that GaTech is offering an online master's degree I am interested in. 

Here in Italy the online degree has the same value as the on-campus degree: we take exams on campus, study online with videos and materials provided by the professor, we have conference sessions with the professors for any questions or we can go visit them in their office. The exams are exactly the same as the on-campus degree, so are the professors.

I was wondering if this is the case in the USA and if doing an online degree will be a limit for me to pursue, in a remote future, a PhD. Should I move to the USA to study (I can work remotely) or I can study here, in Italy, and just go to the USA to take exams?
In my opinion, Georgia Tech's Online Master of Computer Science will not help you get a computer science PhD in the US.  Not because it's online, but because it's a professional master's program.

There are two types of master's degrees in computer science in the US:


Thesis (aka research) masters degrees have a significant research component, in close collaboration with an advisor, leading up to a thesis.  These are generally seen as useful stepping stones to a PhD.
Professional (aka class-based, aka "taught", aka terminal) masters degrees consist entirely of classes.  These are generally not seen as stepping stones to a PhD, because there is no expectation of (and therefore no resources for) research.


Moreover, because of the huge scale (>3000 students) of the OMCS program, having any kind of sustained on-on-one interaction with faculty—which you would need to get strong recommendation letters—is almost impossible.

(I regularly serve on the graduate admissions committee in a top-10 American CS department.)