No, retrospective cohort studies cannot establish causality on their own.
Like other types of observational studies, retrospective cohort studies can suggest associations between an exposure and a health outcome. They cannot prove without a doubt, however, that the exposure studied causes the health outcome.
In particular, retrospective cohort studies suffer from challenges arising from the timing of data collection, research biases like recall bias, and how variables are selected. These lead to low internal validity and the inability to determine causality.