There’s evidence that they’re linked to additional violent thinking, but not a sole factor in making a sane, healthy person into a killer. The former is more nuanced than simply "ban because bad correlation’ though
One thing I wish we could ban are opportunistic suits from hungry law firms that are just hoping that these companies will settle rather than fight an obviously frivolous suit. This is an insult to the civil legal system
So here’s an article on a meta-analysis that covers the a positive correlation. You can also see some newer individual studies that link it to certain violent behaviors such as the treatment of firearms.
Of course, media often overblows such studies because they don’t understand what a strong or weak correlation is and what behaviors these studies are correlating against, which leads to a lot of misunderstanding. Social science may be among the most difficult of the sciences simply because it is measuring patterns with unique biases in their subjects, such as the Hawthorne effect, and extremely high variance that can be difficult to address. For example, the frequency at which and types of games people play now vs 30 years ago is radically different. This is why meta-analyses that examine results across many studies can be valuable, as it often takes repeated studies under changing methodologies and populations to get a proper idea of a social correlation.
I should also emphasize that a positive correlation doesn’t really imply games need to be banned or controlled. In fact the articles linked above mention exactly that – the real concern with a lot of studies is the influence of violent video games on children and their propensity to bully. This doesn’t necessarily imply that video games should be banned, but it can be helpful for guidance to counselors to understand how even minor factors influence social dynamics.