It depends, it depends, and it depends!

As for most questions in business analysis, there isn’t only one answer. Whose job is to create a class diagram depends on the purpose of the class diagram.

First of all, the question implies that there is only one class diagram for a given project: “The Class Diagram”. For the most part, this is not the case. On some projects there may be a multitude of class diagrams while in others there may be none.

Second, the question implies that only one of the person/role on a given project would be task with creating class diagram. This is also not the case! There are many folks (business analyst, systems analysts, developers, etc.) who might have the need to create a class diagram in order to communicate a given concept or to solve a given problem.

So let’s rephrase the question:
“Who would use a class diagram and why?”

The business analyst might chose to create a class diagram in order to model the business domain showing the things of the business (the business domain/industry specific nouns found in the business lingo).

The systems analyst could use a class diagram to develop the logical data model for the system being designed.

The developer may also use a class diagram but for a different purpose: to show the actual classes, interfaces, and types being implemented in a given system.