The Catalan side were awarded two spot-kicks in their recent record-breaking 6-1 victory over Paris Saint-Germain, with Lionel Messi and Neymar converting.
In all, Barca have been awarded 31 Champions League penalties in the competition since 2003, scoring 23 and missing eight.
Bundesliga giants Bayern Munich come second in the number of Champions League penalties taken since 2003-04, scoring 21 and not scoring seven. Bayern last lifted the Champions League trophy in 2013, beating fellow Germans Borussia Dortmund 2-1 in the final at Wembley.
Third in the list are Real Madrid, who progressed into this year's quarter-finals with a 6-2 aggregate win over Italian side Napoli. Los Blancos have taken 26 Champions League penalties since 2003-04, scoring 18 and missing eight.
Sandwiched between the Manchester behemoths are CSKA Moscow, who have had 13 attempts from the spot, scoring nine.
Serie A duo Juventus and AC Milan round off the top 10 of the clubs who have been awarded with the most Champions League penalties, with 11 each, though the former have scored 10 of those while the latter have converted only nine.