B737 CREW HAD UNCOMMANDED RUDDER INPUTS WHILE IN CRUISE.

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LEVEL AT FL330 JUST AFTER EXITING AN AREA OF LIGHT CHOP; WE EXPERIENCED WHAT SEEMED TO BE A QUICK RUDDER KICK. THE MOVEMENT OF THE ACFT WAS MILD; AND NEITHER ONE OF US MADE MENTION OF IT AT THAT TIME. WITHIN THE NEXT 10-15 MINS WE EXPERIENCED THE SAME KICK 2 ADDITIONAL TIMES. NO PEDAL MOVEMENT WAS EVER FELT; HOWEVER; WE DID NOTICE 1/2 - 3/4 NEEDLE DEFLECTION OF THE YAW DAMPER INDICATOR. THE MOVEMENTS OCCURRED WHILE WE WERE IN AND OUT OF LIGHT CHOP. WE BELIEVED THERE WAS A POSSIBILITY THAT THE KICKS WERE TURB INDUCED AND WE DISCUSSED THIS. I THEN TOLD MY FO THAT IF IT HAPPENED AGAIN WE WOULD DIVERT TO THE NEAREST SUITABLE ARPT. AT THIS POINT; I REFED THE FLT HANDBOOK. I THEN PHONE PATCHED DISPATCH AND MAINT CTL AND ADVISED THEM OF THE SIT. MAINT CTL WAS UNSURE OF THE CAUSE AND WE DISCUSSED THE POSSIBILITY OF IT BEING A YAW DAMPER PROB; SINCE THERE WAS NO PEDAL MOVEMENT JUST YAW DAMPER INDICATOR MOVEMENT. I THEN INQUIRED ABOUT ACFT LIMITATIONS WITH THE YAW DAMPER OFF. THEY WERE UNAWARE OF ANY AIRSPD OR ALT LIMITATIONS. I TOLD THEM IF IT HAPPENED AGAIN I WOULD TURN OFF THE YAW DAMPER; SLOW; DSND; AND DIVERT TO THE NEAREST SUITABLE ARPT. NO OBJECTIONS RECEIVED; END OF PATCH. APPROX 25 NM FROM TOP OF DSCNT IT OCCURRED AGAIN. NOTIFIED DISPATCH; SLOWED; DSNDED; AND TURNED OFF YAW DAMPER. THIS TIME WE NOTICED 1 FULL NEEDLE WIDTH DEFLECTION. DECIDED TO DIVERT/CONTINUE TO ZZZ. ASKED FLT ATTENDANTS IF THEY FELT ANYTHING. THEY SAID NO. LANDED UNEVENTFULLY IN ZZZ. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: RPTR SAID ALL PROBS STOPPED WHEN THE YAW DAMPER WAS TURNED OFF. THE CAPT WAS DEBRIEFED BY ACR MAINT; ENGINEERING; FLT SAFETY; AND PLT UNION SAFETY REPRESENTATIVES. THIS ACFT HAD THE OLD ANALOG YAW DAMPER SYS INSTALLED. ACFT ARE BEING MODIFIED TO A NEW DIGITAL YAW DAMPER SYS. THE ACR SENT MAINT TO ZZZ TO MODIFY THIS ACFT WITH THE NEW SYS. NO FURTHER PROBS HAVE BEEN RPTED.