At one point the hail of rocks raining down on officers was so intense that they were forced to retreat in fear of their lives.
Besiris was one of more than 130 people arrested in connection with the two protests that took place and was convicted at a hearing earlier this week.
Srikantharajah Nereshraaj, defending, said the shamed student wished to apologise to the police and community.
He said: "It was inexcusable and unjustifiable. He saw the CCTV and was ashamed and appalled."
In mitigation Mr Nereshraaj said his client had overcome Attention Deficit Hyperactivity Disorder (ADHD) and bipolar disorder to obtain a first class degree.
While at university he had been voted chairman of St Matthias campus, had played competitive rugby and had reinstated a social group which raised money for good causes including bereaved students.
Sentencing him at Bristol Crown Court, Judge Michael Roach said: "Your behaviour on the night in question was disgraceful. It is obvious that that sort of behaviour must attract a custodial sentence."
In a statement issued after the conviction. John Rushforth, UWE Bristol deputy vice-chancellor, added: "The University, whilst upholding students' rights to peaceful protest, does not in any way condone violence.
"There is a university disciplinary process, which can result in a range of outcomes including the withholding of a degree.
"We never prejudge the outcome of that process until the university has considered fully the facts of the case."
A university spokesman added: "The University did not have any prior notification about the detail of the pending conviction.
"The first time that the detail of the conviction came to light was when Patrick Besiris was found guilty at trial yesterday. The University does have very robust procedures for dealing with students in cases like this and does not tolerate violent behaviour from any students."
Besiris is the final offender to be sentenced following the disorder last April and subsequent riots in Bristol in August.
Benjamin Cyster, 18, from Bristol, was sentenced to seven and a half years having been convicted of grievous bodily harm with intent following an incident in which a concrete breeze block was dropped on a police officer from a building.
During the investigation officers examined many hundreds of hours of CCTV footage and appealed for the public's help to identify suspects.
Detective Chief Inspector Will White, who led the investigations, sent out the warning that anyone with plans to bring disorder to the city in the future can expect to be dealt with in the same fashion.
He said: "We will not tolerate disorder of any kind that jeopardises public safety and the safety of police officers carrying out their work.
"Anyone that engages in this type of behaviour should expect to be placed before the courts and dealt with in a robust manner."