Any internet service, including an API, will be able to see the IP address the request originated from. It is reasonable to assume that at least in form of some log file, such information gets records by the API provider.

You have already indicated that you use TOR, which should, at least ideally, hide your real IP from the API service by effectively substituting the IP of the TOR exit node you happen to be using. If that achieves your goal depends on your motivation for hiding it in the first place. Note that TOR is not designed for, and likely not capable of, hiding your real IP from someone doing pervasive internet-wide wire sniffing (NSA, maybe?). Such an adversary would be able to simultaneously observe all traffic at all TOR nodes and correlate incoming and outgoing network activity of TOR nodes to potentially determine what your real IP address is.

You didn't specify why you want to hide your IP from whom exactly, and I'm having one of my unimaginative moments where I cannot come up with a likely scenario why it may be important for you to hide the fact that your computer was involved in looking up publicly accessible information where widespread interest for a whole variety of reasons exists anyways. Hence, I can't judge if for your application, this is sufficiently anonymous and safe (as you asked).

All bitcoin exchanges maintain their own public API for their exchange rate and usually lots of other data, even full order books. If you are happy with delayed third-party data, you can indeed also look at e.g. blockchain.info or bitcoincharts.com.