Can you? Yes, but it might require attribution as per the CC license (kind of joking, kind of serious on this).
Even though rep is probably covered on the license, I think it would be a huge waste of StackExchange's resources to find all of the places on the Internet (and off) that a user's reputation is used and then somehow get them to not use it.
That said, I wouldn't worry about including it (without attribution) in your resume.
The question you should be asking is do you want towant to include your rep on your resume? Is what you've contributed here on StackOverflow (or any StackExchange site for that matter) something that you believe is worth exposing to potential employers?
That's a question that only you can answer, given that you produced the content that you are referencing on your resume.
Also, be aware of the fact that 10K+ users can still see your deleted content (questions and answers), so if the person interviewing you decides that they want to dig deeper into your account, there's a possibility of them coming across something you don't want seen, even if you delete the content.