Yes, Arsenal FC has won an European tournament. They have won the UEFA Cup Winners' Cup in the 1993-1994 season.

The UEFA Cup Winners' Cup was a tournament that featured the winners of various domestic cup competitions across Europe. Arsenal qualified for the tournament by winning the 1993-1994 FA Cup, which was their first major trophy in eight years.

In the final, Arsenal faced off against Italian side Parma at the Parken Stadium in Copenhagen, Denmark. Arsenal won the match 1-0 thanks to a goal from Alan Smith in the 21st minute. The victory marked Arsenal's first ever European trophy.

Other notable performances by Arsenal in European competitions include reaching the final of the UEFA Champions League in the 2005-2006 season, where they lost to Barcelona, and reaching the final of the UEFA Europa League in the 2018-2019 season, where they lost to Chelsea.

Overall, Arsenal has a strong history in European competitions, having reached the final of the UEFA Cup (now the Europa League) twice, and the semi-finals of the Champions League on multiple occasions.