Our second floor master bathroom currently has a sink, toilet and single stall shower. I really want to add a tub as there is room for this but there is no plumbing roughed in for it. Is adding a tub even possible?

Sure - assuming you don't mind tearing out some wall. The easiest would be if the tub could be right next to the back of the shower plumbing.
If you want to draw a picture (or take a photo), and describe what's directly underneath on the first floor, that would help.

You will probably have to relocate supply and drain piping and if a spa tub increase the floor joists due to weight but yes, it is possible since you almost certainly have wood floors.

It is possible, but some renovation is being required. In my opinion, call the plumber and try to pull out some things to fit in tub in your bathroom. Plumbing issues will be there, but after all to have a tub in your bathroom is your desire.