Personally I wouldn’t use “do a role”; it is not good English.

 

“Take a role” is certainly possible, as Nicole says above. 

 

Example: Imagine that we are law students, about to act a mock trial. The organizer might say, “Mai, will you please take the role of judge.  Nicholas, you take the role of counsel for the defense…” 

 

You can also play a role (this is a frequent usage), take up a role, take on a role, assume a role … and so on.

 

You don't normally 'do' a role. You can accept a role, fulfil a role, apply for the role of . . , take on the role of . ., etc., and in theatrical productions act the role of . .

Both of these seem like unusual phrases to me. But I would say that "doing a role" is about completing tasks associated with the role. If the role is in a theater play, it is playing that part. If it is a role in a job, it is about completing the work that role is supposed to do.

"Taking a role" can be one of two things. First, it could simply be the act of accepting the role. More rarely, you might see someone use "taking the role" to mean letting this new role change who they are.