A320 pilot reported the aircraft began to produce a yawing moment during cruise which continued to increase in frequency. Flight diverted and landed safely.

Narrative

At cruise on Aircraft X at 35;000ft; Mach .78 and smooth ride conditions we encountered an aggressive yawing moment to the left estimating 4-5 degrees. The first officer and I would describe the abnormality as if you were to abruptly step on the left rudder pedal and create a quick; hard yaw to the left. There were no ECAM notifications and we checked that there were no abnormalities to any of the system pages. The only normal" indication we noticed was whenever the aircraft yawed to the left; the rudder on the flight control page respectively moved with it. The yawing moment started out with a frequency of every 10-15 seconds and our concern grew as the frequency became closer together. The first officer took over the flight controls and radios and I called dispatch to notify them of the abnormality. They instructed us to check both autopilots and manual flight and unfortunately the condition continued. After disconnecting with dispatch; the frequency continued and we decided the safest option was to divert to the closest airport. I spoke with flight attendants asking if they felt the disturbance and they said they felt it but wasn't that aggressive in the cabin. ZZZ was roughly 50-60NM off our nose so we started the diversion by notifying ATC; going through the diversion checklist; notifying dispatch via ACARS; setting up for the approach; notifying the customers and briefing the flight attendants if condition escalated. Due to it not being a flight control malfunction we did not [request priority handling] but notified ATC that it was an abnormality and we wanted CFR (crash fire rescue) as a precaution. We landed with no incident and taxied safely to the gate in ZZZ."