Hadden was seen wearing a full black tracksuit, a black cap, a scarf around his neck and his face was clearly visible. His black trainers were noted to have white trim.
John McLaughlin, defending, told the court that his client was under the influence of alcohol which affected his recall of events.
He added that Hadden had picked up the bottle in the “spur of the moment” and was “not aiming it at anyone in particular.”
“In the cold light of day, he knows his behaviour was extremely reckless and dangerous and could have caused an injury – he is fortunate no-one was struck,” he added.
He said his client had “got caught up in a fertile atmosphere” and had “literally attended thousands of Rangers matches home and away.”
Sheriff Lorraine Glancy KC told Hadden: “Had the officer not seen the bottle and took evasive action, he could have been struck on the head with it.
“Officers that day kept fans separate, preventing disorder and are to be commended for their bravery and professionalism.
“I consider that a prison sentence is appropriate to deter others from behaving in this way and to reflect the public’s disapproval for behaviour like this at football matches.”