no, Taylor swifts hair is naturally curly, but she does get her hair curled for all her performances and stuff.

here is a picture of her natural hair:
http://4.bp.blogspot.com/_Sm0ZkRMd5I...lor-Swift4.jpg

and then here is when it is curled:
http://www.mimifroufrou.com/scenteds...o-custom_7.jpg