Daniel Begg, 21, of Dundee, admitted culpable and reckless behaviour.
The fan who was struck avoided serious injury in the incident at Pittodrie Stadium on Sunday 25 September.
Begg was fined Â£260 at Aberdeen Sheriff Court. The court refused a Crown motion for a football banning order stopping Begg from attending future games.
Rangers fan Begg was in the away end at Pittodrie.
Police had earlier issued a CCTV appeal to trace him.
A football fan who threw stadium seats at another supporter during an Aberdeen v Rangers game has avoided a ban from matches.