Computer Science and Mathematics form the base of Artificial Intelligence. There is no better degree than computer science to start off with Artificial Intelligence and Its related field like Machine Learning, Neural Networks and others.
Artificial Intelligence basically means how do you make a machine intelligent. Intelligence here means:
The ability to take decision.
The ability to prove direct decision.
The ability to identify flaws in the system.
The ability to learn from the external environment
The ability to apply logic as we humans do.
Once the system possess these mentioned qualities of intelligence you can say that yes a machine is intelligent to some extent.
It involves mathematical concepts of linear algebra and statistics and computer science programming languages which helps you in building this intelligent system.
So if you have a degree in Computer Science, you have the following advantages of pursuing your career in Artificial Intelligence:
You are aware about the basics of AI
You must be well versed with any one of the programming language
Computer Science graduated usually have a good ability to apply logic, so you must be one of them.
Computer Science too consists of various mathematical concepts (though not in detail but yes the basics are covered).
Being a computer science student will help you understand the in depth details about Artificial Intelligence in a much simpler manner. So this will help you in learning and building AI systems much quicker.
And lastly be it any degree if you have the enthusiasm of learning something new and working on it, then you can surely go ahead.