Should I learn C before learning C++?

I love this question - it's like asking "what should I learn first, snowboarding or skiing"? I think it depends if you want to snowboard or to ski. If you want to do both, you have to learn both.

In both sports, you slide down a hill on snow using devices that are sufficiently similar to provoke this question. However, they are also sufficiently different so that learning one does not help you much with the other. Same thing with C and C++. While they appear to be languages sufficiently similar in syntax, the mind set that you need for writing OO code vs procedural code is sufficiently different so that you pretty much have to start from the beginning, whatever language you learn second.

There is no need to learn C before learning C++.

They are different languages. It is a common misconception that C++ is in some way dependent on C and not a fully specified language on its own.

Just because C++ shares a lot of the same syntax and a lot of the same semantics, does not mean you need to learn C first.

If you learn C++ you will eventually learn most of C with some differences between the languages that you will learn over time. In fact its a very hard thing to write proper C++ because intermediate C++ programmers tend to write C/C++.That is true whether or not you started with C or started with C++.

If you know C first, then that is good plus to learning C++. You will start with knowing a chunk of the language. If you do not know C first then there is no point focusing on a different language. There are plenty of good books and tutorials available that start you from knowing nothing and will cover anything you would learn from C which applies to C++ as well.

Please see further reasoning in this answer.