The ROTC program shouldn’t conflict too much with being an Orthodox Jew. Depending on the service, ROTC students don’t have to go to OCS, which is where you run into the most difficulties.
The only problem I see is that there will probably be some training exercises over the weekend.
I think it is safe to say that, unless you are a chaplain, it is nearly impossible to be Shomer Shabbos, all of the time while in the military (and even they can’t do that all the time). Some jobs will allow for it 99% of the time, but there will always be occasions where you have to work or train on Shabbat.