Is cognitive science apart of psychology? If I major in psychology, will it be easy for me to be a cognitive scientist?
It's the other way around: Psychology is a discipline within Cognitive Science, which includes Artificial Intelligence, Neuroscience, and possibly Philosophy of Mind. Research work in Psychology presumably makes you a Cognitive Scientist.
Arnon's answer is right, but I thought it might help to explain why.
Cognitive Science is the study of minds. This can include human minds, other animal minds, and artificial minds. The method could be to study how agents with minds behave in experiments (psychology), to study the physiological properties of biological minds (neuroscience), to create and model synthetic minds (artificial intelligence), to theorize about properties of minds (philosophy), to study the cultures and history of agents with minds (anthropology), and/or to study particular, especially complicated, aspects of minds (linguistics).
Psychology is just one way of approaching the problem (which can tell us quite a bit about minds), but a broader perspective would be needed to get a complete picture of what minds are and how they work.
I agree with Arnon that cognitive science is, by most people's definition, multi-disciplinary. And one of those disciplines included is psychology.
However, if you were to attend a cognitive science conference or read a cognitive science journal, you would see that it mostly includes areas of psychology that broadly relate to cognition.
There are many sub-disciplines of psychology that would not readily identify with cognitive science. For example, clinical psychology, I/O psychology, most of social psychology, most of personality psychology, and so on.
Thus, you might want to think of cognitive science and psychology in terms of partially overlapping Venn Diagrams.
As a final note, we use the term "cognitive sciences" on this site in a very inclusive sense. It is unfortunate that there is no single word that easily captures all that psychology and cognitive science encompasses.