Remus Hamza, 41, of Riverside, Cardiff, was jailed for 12 years in February 2016 for raping the 20-year-old and was also given four years on extended licence.
He took his case to the Court of Appeal in London, arguing this was too severe.
But judges said his appeal was "totally without merit" and gave him an extra 28 days in prison for wasting court time.
Hamza claimed he had consensual sex with his victim, but was found guilty after a trial.
He had also previously exposed himself to three young women in the same area.
The woman was walking home along Museum Avenue in the early hours of 20 September 2015 after losing her friends while on a night out.
Hamza grabbed her and raped her in nearby bushes. He fled after a passer-by spotted him and called the police.
Judge Sarah Munro QC said the victim suffered serious psychological harm as a result of the attack.
Hamza's lawyers argued the crown court judge made the wrong assessment of how serious his crime was and did not take enough account of the fact he would have to serve two thirds of his jail term before his release can be considered.
Dismissing his appeal, Judge Munro said it was "not arguable" the sentence was excessive.
She added: "The provisions relating to early release and licence should be left out of the picture when determining sentence. There is no merit whatsoever in this appeal."

The women were serving as medics at a field hospital in western Aleppo. A mortar struck the hospital on Monday.
A Russian paediatrician seriously wounded in that attack also received the medal.
A fifth Order of Courage went to a Russian colonel wounded elsewhere.
Russia is helping Syrian state forces.
The Kremlin named the five decorated with the Order of Courage for their service in Syria as:
Russia's Tass news agency lists Russia's combat losses so far in the Syria conflict as: 21 military personnel, three helicopters and an Su-24 bomber.
A special forces officer - Senior Lt Alexander Prokhorenko - "died heroically" in March near Palmyra, the Russian government said. He was decorated as a national hero for having called in an air strike against so-called Islamic State (IS) militants, who had surrounded him.
Russia's "anti-terrorism" operation in support of President Bashar al-Assad in Syria began on 30 September 2015.
Russia has mostly carried out intensive air strikes in Syria - including with cruise missiles fired from warships. But Russian special forces and military advisers are also helping Syrian government troops on the ground.
According to a Reuters investigation, Russian private contractors or mercenaries are also fighting in Syria, in support of the official military contingent.

Police have been searching the site in Milton, Cambridgeshire, for five weeks.
Despite a high-profile missing persons campaign, it is thought by police he ended up in a bin lorry.
Mr Mckeague's father Martin said it was "breathtaking" to see how much waste officers have combed through.
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He has been to the site five times and is staying in a nearby campsite with his wife Trish.
"It's heartbreaking to think when you are there Corrie could be under foot," he said.
"Everything leads to Corrie being there and when I'm looking at and watching these guys rake through, I know the police wouldn't be here going through all these tonnes of rubbish if they didn't expect Corrie to be there."
Mr Mckeague, from Dunfermline in Fife, vanished while on a night out in Bury St Edmunds, Suffolk, on 24 September.
He was last seen on CCTV at about 03:25 BST.
A bin lorry collected refuse a short time later from the area the RAF Honington gunner was last seen.
Suffolk Police said officers were trawling through 60 tonnes a day at the site in Milton, near Cambridge.
The search is now in its fifth week and is expected to take up to 10.
A rapist who attacked a student as she walked home during freshers' week has been given an extended sentence.
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Five Russian soldiers have received the "Order of Courage" from President Vladimir Putin, including a colonel and two women sergeants killed by Syrian rebel shelling of Aleppo.
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The father of missing airman Corrie Mckeague, who is camping near a landfill site as police search for a body, said it is "heartbreaking" to think his son is buried there.