Is it normal to CC my professor when they introduced me to someone?
Most faculty are curious and would like to know what their students are doing, therefore you should CC them. If you CC them, they don't have to ask you if you sent the email.  If you CC them, they have the opportunity to clarify what you have written.

Some faculty consider deleting an email to be an unpleasant chore.  If your supervisor is one of those people, do not CC them.  

Otherwise it is a matter of individual preference.  Few people consider it rude to CC or rude to not CC.