Air carrier Captain reported while taxing into the gate they had to stop the aircraft to avoid colliding with a tug with bag carts moving at a high speed through the gate protected safety zone.

Narrative

We pulled onto the line at Gate X in ZZZ. There were Marshallers in the gate; and they were milling around as usual in ZZZ. As I started in; we both noticed a tug with bag carts in tow heading toward us at a very high speed on the access road. I slowed a bit in case he was going to cut it close before veering off into the next gate or something similar; but instead he cut right in front of us as if we weren't even there. I turned on all our lights and blasted the tug a with a million candlepower of landing lights as I hit the brakes to avoid running into him. The driver didn't alter his course one bit; still blasting right through our parking zone at high speed. This was absolutely unsafe in every way imaginable. The driver was either not paying attention or chose to cross in front of a moving aircraft in the protected zone of the parking gate. The Employee; frankly; needs to never operate a moving vehicle on airport grounds again. His/her actions were totally irresponsible and put an aircraft in jeopardy. We have enough on our plate already without having to wonder if our own tug drivers are trying to run into our aircraft. As an airline; we claim to hold safety up as our highest goal; and this is an egregious example of the exact opposite. We slowed the aircraft; as I anticipated some sort of corrective action on the driver's part. I should have assumed that there would be none and not counted on the good graces of the cart driver to notice and avoid a collision. Next time I will completely stop; assume the worst; and let Ground Ops sort things out.