David Craig, 24, was also banned from all football grounds in the UK for three years.
Craig, from Paisley, was snared after he posted hate-filled messages about the Celtic manager including 'Neil Lennon dead man !!!!!!!! UVF' on his Facebook page in March last year.
Sentencing Craig, Sheriff Martin Jones QC told him that his actions were "vile and hateful", adding, "There is no place for them in an enlightened society."
The sheriff said that Craig's posting came amid escalating sectarian hostility after a powderkeg Old Firm match on March 2 last year.
He added: "You placed an image and comments which continued to fuel that atmosphere and access to your site was fully available to the public."
He said the bullet-riddled picture of Celtic manager Neil Lennon, a Catholic from Northern Ireland, prompted responses from others.
Sheriff Jones said Craig's behaviour needed to be marked with a jail sentence.
The fact David had already spent the equivalent of nine months on remand was taken into account in sentencing.
At an earlier appearance at Glasgow Sheriff Court, Craig admitted behaving in a threatening or abusive manner likely to cause fear and alarm by posting images and messages of an offensive, threatening and sectarian nature.
Craig's sentence comes on the day that new anti-sectarian legislation becomes law, but he was charged under the old legislation.