Ziobro made his first international appearance at the age of 15 at an FIS Cup show jumping event in Einsiedeln, Switzerland . In this competition he moved in the next few years, before he was used for the first time on January 23, 2010 in the Austrian Bischofshofen in a Continental Cup competition . Since then he has mainly jumped in this second-rate series of competitions.
After Ziobro collected his first points at a higher level in the Summer Grand Prix at the jumping in Hakuba and Almaty in summer 2011 , he was able to qualify for a World Cup jumping for the first time in his career on November 27, 2011 in Kuusamo, Finland , when he was 46 ., however, he clearly missed the points. On the same day, he was in the Polish team for the only time in a team competition and finished seventh with his teammates. By the end of 2011, he was able to take part in four other World Cup competitions, but without making it into the points - his best placement was a 39th place on December 3, 2012 in Lillehammer . In calendar year 2012, he has only been nominated in January in the domestic Zakopane once for the national group of the local World Cup competition, but failed already in qualifying, otherwise he jumped only in the Continental Cup, where he on September 27 in Engelberg his first podium finish in third reached. It was not until the jumping competitions in Poland at the beginning of 2013 that he got the chance again to qualify for World Cup competitions - again via the national group. When jumping in Wisła he failed in the qualification, but on January 12, 2013 in Zakopane he profited from the disqualification of the Czech Lukáš Hlava , moved up to the 40th place in the qualification and thus barely entered the competition. There he earned his first eleven World Cup points as 20th. Back in the Continental Cup, he achieved his best result so far in this series of competitions on March 8, 2013 in Vikersund with second place.
On September 8, 2013, Ziobro secured his first national championship title on the large hill in Zakopane .
On December 21, 2013 he celebrated his first World Cup victory on the Gross-Titlis-Schanze in Engelberg and confirmed this success with third place the following day on the same hill. At his first Olympic Winter Games in Sochi in 2014 , he jumped from the normal hill to 13th place, before he was 15th on the large hill. With his teammates Maciej Kot , Piotr Żyła and Kamil Stoch , he barely missed a medal in the final team competition and finished fourth.
On January 10, 2015, Ziobro celebrated his first Continental Cup victory on the Malinka in Wisła .
In January 2018, Ziobro announced that he was temporarily suspending his career. He combined this with violent allegations against those responsible for the Polish Ski Association, who had not nominated him for upcoming competitions in the Continental Cup.