Air carrier pilot reported a ground conflict with a large UAS during taxi.

Narrative

We had just operated Flt ABCD into ZZZ and we were in the process of turning the aircraft to operate Flt ABCE back to ZZZ1 when we heard an unfamiliar call sign on the CTAF making traffic pattern announcements (ZZZ tower was closed for the night). The callsign in question was a little difficult to make out. Shortly thereafter the flight was closed out and we announced our pushback onto taxiway 1 and our intent to use runway XX for departure. During the pushback the mysterious aircraft announced that he was back taxiing on runway XX and would clear at taxiway 2. At that point we were abeam taxiway 2. I looked out of my left window and was more than a little surprised to see a military MQ-9 Reaper drone sitting on the active runway; waiting to exit onto taxiway 2. I instructed my pushback crew to push us deep past taxiway 2 so the drone would have enough room to clear the runway. In addition; I warned my pushback crew to use caution as the drone would be operating in close proximity to us. We announced our intention to push past taxiway 2 and the drone operator responded that he had us in sight and would clear the runway. I did then observe that the sensor turret on the chin of the drone was pointed at us which seemed to be how the drone operator was able to see us. The drone then proceeded down taxiway 1 ahead of us. We disconnected from the pushback and announced our taxi. As we started down the taxiway we contacted ZZZ center for IFR release. ZZZ center advised that he was unable to release us as the drone had not yet cancelled its IFR flight plan. We contacted the drone operator over the CTAF and requested that he cancel with ZZZ. He complied with our request and ZZZ released us. We continue to follow the drone down taxiway 1; assuming that he was going to pull into one of the hangars to the right of the taxiway. This was an incorrect assumption as the drone proceeded all the way down to the approach end of runway XX and came to a stop short of the runway. We pulled up behind the drone at which point my taxi lights illuminated the drone and gave us our first really good look at it. I was quite alarmed to discover that the drone had two underwing weapon pylons with each pylon occupied by a brace of anti-tank missiles and here I was pulled up short directly behind this fully armed and un-safed aircraft. I could; at this point; clearly identify the yellow markings on the missiles indicating that they were live ordinance with a High Explosive fill. After a brief halt; the drone crossed the active runway and appeared to head for a small; partially lit parking area on the far side of the runway. We then announced our departure and took off uneventfully from runway XX.