No, a CV (also commonly called a resume) does not have to be size 12 font.
Readability is the most important thing to consider when choosing the font size on your CV, so while the 12-point font is the standard size for most CV’s, anywhere between 10-12 point font is acceptable if it is easy to read.
Picking the right size for your CV depends on what font you are using. Some fonts look great at 12 points, yet another font might look too big or small. How much extra space you have on the page can also lead you to change your CV’s font size. If you are trying to fit more information onto a page, it makes sense to decrease your font size slightly rather than remove relevant text.