Buszek was born in Dębica, Poland. He is married to Aleksandra. In September 2016, Buszek and his wife announced via social media they are expecting their first child. On October 18, 2016 their son was born and Rafał announced his arrival and added photo via Instagram in February 2017. In May 2018, their daughter was born.
Buszek debuted in the Polish national team on May 29, 2014 against Brazil (0-3).[4] He was appointed by coach Stephane Antiga on World League 2014. Initially, he was supposed to be a deputy to principal players during matches in Brazil, but after a few victories (amongst others, the winning match with Brazil on May 31, 2014) he became a favorite to play at the World Championship.[5] On August 16, 2014 Buszek was appointed to the squad at the World Championship held in Poland.[6][7] On September 21, 2014 he won the title of World Champion 2014 as part of this team.[8][9][10] On October 27, 2014 he received a state award granted by the Polish President Bronisław Komorowski – Gold Cross of Meritfor outstanding sports achievements and worldwide promotion of Poland.[11]