I really like this girl and she's 17, she likes me and I like her but the only problem is I don't know if its legal, I just turned 21 and I live in the state of PA

Absolutely YES

There is no "dating" laws, there are laws about having sex with minors and the age of consent is different in various states, here in Georgia it is 18, *** can't tell you your state at the moment, lost all my bookmarks yesterday

In Pennsylvania it does not appear that it is illegal. You can check it out on this website. A table of worldwide ages of consent, including US states (http://www.avert.org/aofconsent.htm)

Now, do her parents approve?

Dating in and of itself is never illegal, it is the sexual activity, including kissing, that is considered legal or illegal.