A section of the Celtic support unfurled paramilitary-style banners during the club’s 4-0 victory at Celtic Park.
The banners led to Celtic being fined €23,000 (£20,615) by Uefa.
Police Scotland said 12 men aged between 18 and 49 were arrested over “banners and material” at the match.
They are expected to appear in court on 24 August and 1 September.
Several large banners were displayed in the section of the stadium occupied by the Green Brigade supporters group during the match in Glasgow on 19 July.
One showed a face in paramilitary-style black beret and dark glasses, while the other showed Rodgers alongside the slogan “Rodgers at work” – an apparent play on the IRA’s “sniper at work” signs in South Armagh during the 1990s.
Other banners formed the phrase “Brendan’s Undefeated Army” – another play on an IRA slogan.
Celtic subsequently announced that it would be closing the Green Brigade section for the club’s next two matches.
Uefa rules prohibit the use of “any message that is not fit for a sports event, particularly messages that are of a political, ideological, religious, offensive or provocative nature”.
A statement from Celtic released at the time said: “Any support for a paramilitary or proscribed terrorist organisation has no place at Celtic Park.
“The club has been consistent in condemning such conduct on the very few occasions in the past when it has occurred at Celtic Park. It is unfortunate that such a small minority of the crowd at Celtic Park behaved in such a way.
“We know that the Celtic support will join us in condemning such behaviour.”
The Uefa fine was Celtic’s 11th punishment in six years relating to misconduct from supporters during European ties.
A Linfield fan was last week banned for life by the Belfast-based club after being convicted of sectarian singing during the match, which was the second leg of the qualifying tie.
Trouble in the first leg in Belfast led to Linfield being handed a partial stadium closure for their next European tie and an £8,850 fine following incidents at Windsor Park.
Uefa imposed the penalties after objects were thrown at Celtic players.