The 23-year-old moves to Ashton Gate on a year-long loan deal from Ujpest FC.
If the loan proves to be a success, the Robins have the option to sign Vasko on a permanent three-year deal.
Vasko has spent the last four years with Ujpest after previously playing for Vassas.
He also had a loan spell with FC Tatabanya during the 2004-05 campaign.