B737-800 Captain reported a track deviation occurred following a wake vortex encounter in cruise flight.

Narrative

During cruise flight at FL370 we had been encountering continuous choppy air. As we crossed over the Chesapeake Bay Area just north of Norfolk VOR; I noticed that there was a contrail directly in front of our aircraft that we were flying directly within. I assumed that perhaps we were in the wake turbulence of another aircraft and requested a right deviation of up to 3 miles right of course to see if we could get out of the wake turbulence that we appeared to be flying into. Washington ATC questioned why I wanted the right deviation and I advised them that there was a cloud we were attempting to avoid. The right deviation was approved and I was told to proceed to ZJAAY after deviation and I selected a 20 to 25 degree heading to the right of course to exit the bumpy air. After approximately 2 minutes of the heading we had exited the choppy air and I selected a heading back to the left to start heading back over towards our original course line and then proceeded to input into the FMS the Direct to JZAAY point as directed by ATC. The airplane after I selected LNAV began a right turn to proceed directly to JZAAY and then the controller asked us in a frantic voice; 'where are you going'. I advised him that we were direct to ZJAYY and he replied 'NO YOURE NOT'. I advised him that we were in the turn directly to ZJAAY and then he advised a [other carrier] flight to descend to FL360 and then advised me that I had a possible pilot deviation and standby to copy a number. I then received the number and asked ATC to pull the tapes. I noticed that there was an aircraft approximately 5 miles away from me heading southbound at FL 370 wrong direction but verified that I never deviated left of my original course line on the airway. We never even came close to the other aircraft according to our TCAS system and never received a traffic call or a TA or RA call from the TCAS system.Cause: Looking back at this I might have put in an aggressive turn back towards the original course while I input data into the FMS but I am pretty certain that we never deviated left of our original course and by the time the ATC controller asked me where I was going I was already heading directly to ZJAAY as directed.Suggestions: Perhaps always putting the direct to point in the FMS and selecting that instead of using heading select may have not appeared to be such a large turn back towards the original course.