Date: 201810
Local time of day: 1801-2400
Location: ZZZ.Airport, US
Flight conditions: VMC
Weather elements / visibility: Rain
Aircraft: A319
Operator: Air Carrier
Operating under: Part 121
Flight plan: IFR
Mission: Passenger
Flight phase: Taxi
Reporter organization: Air Carrier
Reporter function: Captain; Pilot Flying
Reporter qualification: Flight Crew Instrument; Flight Crew Air Transport Pilot (ATP); Flight Crew Multiengine
Human factors: Confusion; Situational Awareness
Second reporter function: Pilot Not Flying; First Officer
Anomaly: Deviation / Discrepancy - Procedural Published Material / Policy; Ground Event / Encounter Vehicle
Detector: Person Ground Personnel
When detected: Taxi
Result: Aircraft Aircraft Damaged; General Maintenance Action
Contributing factors: Human Factors; Weather
Primary problem: Human Factors

Narrative: While parking at gate at ZZZ; both engines were running as we had just exited the runway 30-60 seconds prior; after landing Runway XXR. As I approached the parking envelope I noticed a wing walker on the left wing and a Marshaller standing in the back of the push back tug parked in position for the next push back; both had lighted wands. I assume she was in the back of the tug for better vision of the parking envelope. I noticed a ramp person running from a just parked aircraft to our right and assumed he was picking up right wing walker duties. I noticed the tug and carts parked to our right; inside the parking envelope; but equipment inside the parking box is not unusual; and assumed it was prepositioned there for a purpose. I had a Marshaller guiding me in and two wing walkers (I thought). They can clearly see any obstruction better than I can; and I continued to follow parking guidance. I was moving very slow as there was a lot of activity on the ramp; it was late at night and starting to rain. While following the Marshaller's guidance; I felt the aircraft slightly yaw to the right; thinking I hit a wheel chalk I set the brakes and had the First Officer shut down both engines. We were still 5 or so feet short of the jet bridge so the Marshaller continued to marshall us forward. I could not communicate with ground personnel; via company ops radio; or inter phone. When they realized why I wasn't moving there was much confusion; yet no contact with us. I did not know I had hit the tug; again I assumed it was a prepositioned wheel chalk. I made a PA indicating it would be a few minutes to get the jet bridge up to the aircraft. It took 3-4 minutes to attach the jet bridge. After running the parking checklist I was able to exit the aircraft to see what had happened. Only then did I realize I hit a parked tug with the right engine. Damage to the engine seemed limited to dents to the engine intake; however it was running when it hit so; no way of knowing if there was any FOD damage. After deboarding the passengers off the aircraft; I called the Chief Pilot; Dispatch; Technical Support Maintenance Control and the [union] hotline. We made a logbook write up indicating we made contact with a ground tug with the running right engine. It was determined we needed to be drug and alcohol tested. It took about an hour to arrange the drug test through the Chief Pilot. The Chief Pilot contacted me with location and contacts for the drug/alcohol test; and indicated the on sight manager needs to accompany us to the testing site. I called on her cell phone to relay this; she indicated she was aware she needed to accompany us and that the two Marshaller's would be going as they were required to be tested as well; I don't know who required them to be tested; [The Manager] never volunteered that information. We made it to the testing site; concluded the testing and got a taxi to the hotel.


Second narrative: [Report narrative contained no additional information.]


Synopsis: A319 flight crew reported that while being marshalled into the gate area; the aircraft made contact with a ground vehicle; damaging an engine cowl.