When you make a call over the Internet it is called Voice Over Internet Protocol or VOIP call.
It is fairly cheap compared to the regular operators we use for phone calls. Although it cannot be considered reliable. But then again you can even make anonymous phone calls using these services.
EvaPhone and Call2Friends provide these services for a limited time for free that too everyday.
You can even consider buying subscription of these services which is fairly cheap and has no expiration. That is pay per use.Just know that even though these calls are anonymous they are anonymous to some extent only and you identity can be traced through them.