This claim is incredibly popular, and is widely believed to be true. There has been lots of research done on the topic, and several sources have claimed there is a connection. However, other sources have not only argued against that claim, but offered reasoning for the false results.
In an article posted by the University of Oxford, several researchers of their school clams there is no relationship between aggressive behavior in teens and the amount of time spent playing violent video games. For their research, they asked parents and carers to speak on the chid’s behavior, and had the video games classified using official rating systems (Pan European Game Information and Entertainment Software Rating Board).
There are a few extra points to take from this article. Of course, the fact their research was done with British kids can lead to a lack of external validity. However, even if these results are questionable, the article also provides reasons to doubt other studies as well. Unlike this study, others have relied on self-reported data from teenagers. They also cite researcher bias as a reason for possible incorrect findings.
In the end, this article doesn’t connect violent video games to violent behavior, but does point out how other situations, such as trash-talking or stress can lead to teenagers getting more aggressive (But this can result from most video games, regardless of genre).